{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0001","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-3)t+(-12)；g:R→R，g(t)=(-2)t+(6)。在 x=-12 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-42","explanation_zh":"先求 f(x)=24，再求 g(f(x))=-42，所以答案為 -42。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304001,"parameters":{"operation":"g_after_f","a":-3,"b":-12,"c":-2,"d":6,"x":-12,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-3,\"b\":-12,\"c\":-2,\"d\":6,\"operation\":\"g_after_f\",\"x\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0002","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-2)t+(-11)；g:R→R，g(t)=(-1)t+(5)。在 x=-11 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-6","explanation_zh":"先求 f(x)=11，再求 g(f(x))=-6，所以答案為 -6。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304002,"parameters":{"operation":"g_after_f","a":-2,"b":-11,"c":-1,"d":5,"x":-11,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-2,\"b\":-11,\"c\":-1,\"d\":5,\"operation\":\"g_after_f\",\"x\":-11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0003","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-1)t+(-10)；g:R→R，g(t)=(0)t+(4)。在 x=-10 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"4","explanation_zh":"先求 f(x)=0，再求 g(f(x))=4，所以答案為 4。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304003,"parameters":{"operation":"g_after_f","a":-1,"b":-10,"c":0,"d":4,"x":-10,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-1,\"b\":-10,\"c\":0,\"d\":4,\"operation\":\"g_after_f\",\"x\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0004","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(0)t+(-9)；g:R→R，g(t)=(1)t+(3)。在 x=-9 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-6","explanation_zh":"先求 f(x)=-9，再求 g(f(x))=-6，所以答案為 -6。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304004,"parameters":{"operation":"g_after_f","a":0,"b":-9,"c":1,"d":3,"x":-9,"semantic_template":"qf-composition-affine-evaluation/{\"a\":0,\"b\":-9,\"c\":1,\"d\":3,\"operation\":\"g_after_f\",\"x\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0005","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(-8)；g:R→R，g(t)=(2)t+(2)。在 x=-8 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-30","explanation_zh":"先求 f(x)=-16，再求 g(f(x))=-30，所以答案為 -30。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304005,"parameters":{"operation":"g_after_f","a":1,"b":-8,"c":2,"d":2,"x":-8,"semantic_template":"qf-composition-affine-evaluation/{\"a\":1,\"b\":-8,\"c\":2,\"d\":2,\"operation\":\"g_after_f\",\"x\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0006","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(2)t+(-7)；g:R→R，g(t)=(-2)t+(1)。在 x=-7 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"43","explanation_zh":"先求 f(x)=-21，再求 g(f(x))=43，所以答案為 43。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304006,"parameters":{"operation":"g_after_f","a":2,"b":-7,"c":-2,"d":1,"x":-7,"semantic_template":"qf-composition-affine-evaluation/{\"a\":2,\"b\":-7,\"c\":-2,\"d\":1,\"operation\":\"g_after_f\",\"x\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0007","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(3)t+(-6)；g:R→R，g(t)=(-1)t+(0)。在 x=-6 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"24","explanation_zh":"先求 f(x)=-24，再求 g(f(x))=24，所以答案為 24。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304007,"parameters":{"operation":"g_after_f","a":3,"b":-6,"c":-1,"d":0,"x":-6,"semantic_template":"qf-composition-affine-evaluation/{\"a\":3,\"b\":-6,\"c\":-1,\"d\":0,\"operation\":\"g_after_f\",\"x\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0008","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-3)t+(-5)；g:R→R，g(t)=(0)t+(-1)。在 x=-5 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-1","explanation_zh":"先求 f(x)=10，再求 g(f(x))=-1，所以答案為 -1。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304008,"parameters":{"operation":"g_after_f","a":-3,"b":-5,"c":0,"d":-1,"x":-5,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-3,\"b\":-5,\"c\":0,\"d\":-1,\"operation\":\"g_after_f\",\"x\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0009","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-2)t+(-4)；g:R→R，g(t)=(1)t+(-2)。在 x=-4 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"2","explanation_zh":"先求 f(x)=4，再求 g(f(x))=2，所以答案為 2。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304009,"parameters":{"operation":"g_after_f","a":-2,"b":-4,"c":1,"d":-2,"x":-4,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-2,\"b\":-4,\"c\":1,\"d\":-2,\"operation\":\"g_after_f\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0010","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-1)t+(-3)；g:R→R，g(t)=(2)t+(-3)。在 x=-3 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-3","explanation_zh":"先求 f(x)=0，再求 g(f(x))=-3，所以答案為 -3。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304010,"parameters":{"operation":"g_after_f","a":-1,"b":-3,"c":2,"d":-3,"x":-3,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-1,\"b\":-3,\"c\":2,\"d\":-3,\"operation\":\"g_after_f\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0011","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(0)t+(-2)；g:R→R，g(t)=(-2)t+(-4)。在 x=-2 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"0","explanation_zh":"先求 f(x)=-2，再求 g(f(x))=0，所以答案為 0。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304011,"parameters":{"operation":"g_after_f","a":0,"b":-2,"c":-2,"d":-4,"x":-2,"semantic_template":"qf-composition-affine-evaluation/{\"a\":0,\"b\":-2,\"c\":-2,\"d\":-4,\"operation\":\"g_after_f\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0012","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(-1)；g:R→R，g(t)=(-1)t+(-5)。在 x=-1 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-3","explanation_zh":"先求 f(x)=-2，再求 g(f(x))=-3，所以答案為 -3。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304012,"parameters":{"operation":"g_after_f","a":1,"b":-1,"c":-1,"d":-5,"x":-1,"semantic_template":"qf-composition-affine-evaluation/{\"a\":1,\"b\":-1,\"c\":-1,\"d\":-5,\"operation\":\"g_after_f\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0013","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(2)t+(0)；g:R→R，g(t)=(0)t+(-6)。在 x=0 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-6","explanation_zh":"先求 f(x)=0，再求 g(f(x))=-6，所以答案為 -6。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304013,"parameters":{"operation":"g_after_f","a":2,"b":0,"c":0,"d":-6,"x":0,"semantic_template":"qf-composition-affine-evaluation/{\"a\":2,\"b\":0,\"c\":0,\"d\":-6,\"operation\":\"g_after_f\",\"x\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0014","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(3)t+(1)；g:R→R，g(t)=(1)t+(6)。在 x=1 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"10","explanation_zh":"先求 f(x)=4，再求 g(f(x))=10，所以答案為 10。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304014,"parameters":{"operation":"g_after_f","a":3,"b":1,"c":1,"d":6,"x":1,"semantic_template":"qf-composition-affine-evaluation/{\"a\":3,\"b\":1,\"c\":1,\"d\":6,\"operation\":\"g_after_f\",\"x\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0015","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-3)t+(2)；g:R→R，g(t)=(2)t+(5)。在 x=2 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-3","explanation_zh":"先求 f(x)=-4，再求 g(f(x))=-3，所以答案為 -3。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304015,"parameters":{"operation":"g_after_f","a":-3,"b":2,"c":2,"d":5,"x":2,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-3,\"b\":2,\"c\":2,\"d\":5,\"operation\":\"g_after_f\",\"x\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0016","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-2)t+(3)；g:R→R，g(t)=(-2)t+(4)。在 x=3 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"10","explanation_zh":"先求 f(x)=-3，再求 g(f(x))=10，所以答案為 10。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304016,"parameters":{"operation":"g_after_f","a":-2,"b":3,"c":-2,"d":4,"x":3,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-2,\"b\":3,\"c\":-2,\"d\":4,\"operation\":\"g_after_f\",\"x\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0017","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-1)t+(4)；g:R→R，g(t)=(-1)t+(3)。在 x=4 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"3","explanation_zh":"先求 f(x)=0，再求 g(f(x))=3，所以答案為 3。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304017,"parameters":{"operation":"g_after_f","a":-1,"b":4,"c":-1,"d":3,"x":4,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-1,\"b\":4,\"c\":-1,\"d\":3,\"operation\":\"g_after_f\",\"x\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0018","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(0)t+(5)；g:R→R，g(t)=(0)t+(2)。在 x=5 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"2","explanation_zh":"先求 f(x)=5，再求 g(f(x))=2，所以答案為 2。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304018,"parameters":{"operation":"g_after_f","a":0,"b":5,"c":0,"d":2,"x":5,"semantic_template":"qf-composition-affine-evaluation/{\"a\":0,\"b\":5,\"c\":0,\"d\":2,\"operation\":\"g_after_f\",\"x\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0019","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(6)；g:R→R，g(t)=(1)t+(1)。在 x=6 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"13","explanation_zh":"先求 f(x)=12，再求 g(f(x))=13，所以答案為 13。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304019,"parameters":{"operation":"g_after_f","a":1,"b":6,"c":1,"d":1,"x":6,"semantic_template":"qf-composition-affine-evaluation/{\"a\":1,\"b\":6,\"c\":1,\"d\":1,\"operation\":\"g_after_f\",\"x\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0020","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(2)t+(7)；g:R→R，g(t)=(2)t+(0)。在 x=7 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"42","explanation_zh":"先求 f(x)=21，再求 g(f(x))=42，所以答案為 42。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304020,"parameters":{"operation":"g_after_f","a":2,"b":7,"c":2,"d":0,"x":7,"semantic_template":"qf-composition-affine-evaluation/{\"a\":2,\"b\":7,\"c\":2,\"d\":0,\"operation\":\"g_after_f\",\"x\":7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0021","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(3)t+(8)；g:R→R，g(t)=(-2)t+(-1)。在 x=8 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-65","explanation_zh":"先求 f(x)=32，再求 g(f(x))=-65，所以答案為 -65。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304021,"parameters":{"operation":"g_after_f","a":3,"b":8,"c":-2,"d":-1,"x":8,"semantic_template":"qf-composition-affine-evaluation/{\"a\":3,\"b\":8,\"c\":-2,\"d\":-1,\"operation\":\"g_after_f\",\"x\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0022","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-3)t+(9)；g:R→R，g(t)=(-1)t+(-2)。在 x=9 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"16","explanation_zh":"先求 f(x)=-18，再求 g(f(x))=16，所以答案為 16。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304022,"parameters":{"operation":"g_after_f","a":-3,"b":9,"c":-1,"d":-2,"x":9,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-3,\"b\":9,\"c\":-1,\"d\":-2,\"operation\":\"g_after_f\",\"x\":9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0023","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-2)t+(10)；g:R→R，g(t)=(0)t+(-3)。在 x=10 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-3","explanation_zh":"先求 f(x)=-10，再求 g(f(x))=-3，所以答案為 -3。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304023,"parameters":{"operation":"g_after_f","a":-2,"b":10,"c":0,"d":-3,"x":10,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-2,\"b\":10,\"c\":0,\"d\":-3,\"operation\":\"g_after_f\",\"x\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0024","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(-1)t+(11)；g:R→R，g(t)=(1)t+(-4)。在 x=11 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"-4","explanation_zh":"先求 f(x)=0，再求 g(f(x))=-4，所以答案為 -4。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304024,"parameters":{"operation":"g_after_f","a":-1,"b":11,"c":1,"d":-4,"x":11,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-1,\"b\":11,\"c\":1,\"d\":-4,\"operation\":\"g_after_f\",\"x\":11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-affine-evaluation-0025","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"明示線性表達式的合成","stem_zh":"明示總函數 f:R→R，f(t)=(0)t+(12)；g:R→R，g(t)=(2)t+(-5)。在 x=12 時，求 (g∘f)(x) 的精確值。","answer":{"kind":"short_text","value":"19","explanation_zh":"先求 f(x)=12，再求 g(f(x))=19，所以答案為 19。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["先內後外","精確代入"]},"variant":{"family_id":"qf-composition-affine-evaluation","seed":202609304025,"parameters":{"operation":"g_after_f","a":0,"b":12,"c":2,"d":-5,"x":12,"semantic_template":"qf-composition-affine-evaluation/{\"a\":0,\"b\":12,\"c\":2,\"d\":-5,\"operation\":\"g_after_f\",\"x\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0001","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-12, -11, -10}、B={-2, 0, 3}、C={-1, 0, 4}；f 表=[(-12, -2), (-11, 0), (-10, 3)]，g 表=[(-2, -1), (0, 4), (3, 0)]。求 (g∘f)(-12)。","answer":{"kind":"short_text","value":"-1","explanation_zh":"先取 f(-12)，再以其中間值查 g 表；中間值與結果為 -2, -1。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304101,"parameters":{"operation":"table_evaluate","A":[-12,-11,-10],"B":[-2,0,3],"C":[-1,0,4],"F":[[-12,-2],[-11,0],[-10,3]],"G":[[-2,-1],[0,4],[3,0]],"x":-12,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-12,-11,-10],\"B\":[-2,0,3],\"C\":[-1,0,4],\"F\":[[-12,-2],[-11,0],[-10,3]],\"G\":[[-2,-1],[0,4],[3,0]],\"operation\":\"table_evaluate\",\"x\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0002","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-11, -10, -9}、B={-3, 0, 4}、C={-3, 0, 6}；f 表=[(-11, 0), (-10, 4), (-9, -3)]，g 表=[(-3, 0), (0, -3), (4, 6)]。求 (g∘f)(-10)。","answer":{"kind":"short_text","value":"6","explanation_zh":"先取 f(-10)，再以其中間值查 g 表；中間值與結果為 4, 6。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304102,"parameters":{"operation":"table_evaluate","A":[-11,-10,-9],"B":[-3,0,4],"C":[-3,0,6],"F":[[-11,0],[-10,4],[-9,-3]],"G":[[-3,0],[0,-3],[4,6]],"x":-10,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-11,-10,-9],\"B\":[-3,0,4],\"C\":[-3,0,6],\"F\":[[-11,0],[-10,4],[-9,-3]],\"G\":[[-3,0],[0,-3],[4,6]],\"operation\":\"table_evaluate\",\"x\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0003","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-10, -9, -8}、B={-4, 0, 5}、C={-5, 0, 8}；f 表=[(-10, 5), (-9, -4), (-8, 0)]，g 表=[(-4, 8), (0, 0), (5, -5)]。求 (g∘f)(-8)。","answer":{"kind":"short_text","value":"0","explanation_zh":"先取 f(-8)，再以其中間值查 g 表；中間值與結果為 0, 0。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304103,"parameters":{"operation":"table_evaluate","A":[-10,-9,-8],"B":[-4,0,5],"C":[-5,0,8],"F":[[-10,5],[-9,-4],[-8,0]],"G":[[-4,8],[0,0],[5,-5]],"x":-8,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-10,-9,-8],\"B\":[-4,0,5],\"C\":[-5,0,8],\"F\":[[-10,5],[-9,-4],[-8,0]],\"G\":[[-4,8],[0,0],[5,-5]],\"operation\":\"table_evaluate\",\"x\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0004","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-9, -8, -7}、B={-5, 0, 6}、C={-7, 0, 10}；f 表=[(-9, -5), (-8, 0), (-7, 6)]，g 表=[(-5, -7), (0, 10), (6, 0)]。求 (g∘f)(-9)。","answer":{"kind":"short_text","value":"-7","explanation_zh":"先取 f(-9)，再以其中間值查 g 表；中間值與結果為 -5, -7。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304104,"parameters":{"operation":"table_evaluate","A":[-9,-8,-7],"B":[-5,0,6],"C":[-7,0,10],"F":[[-9,-5],[-8,0],[-7,6]],"G":[[-5,-7],[0,10],[6,0]],"x":-9,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-9,-8,-7],\"B\":[-5,0,6],\"C\":[-7,0,10],\"F\":[[-9,-5],[-8,0],[-7,6]],\"G\":[[-5,-7],[0,10],[6,0]],\"operation\":\"table_evaluate\",\"x\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0005","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-8, -7, -6}、B={-6, 0, 7}、C={-9, 0, 12}；f 表=[(-8, 0), (-7, 7), (-6, -6)]，g 表=[(-6, 0), (0, -9), (7, 12)]。求 (g∘f)(-7)。","answer":{"kind":"short_text","value":"12","explanation_zh":"先取 f(-7)，再以其中間值查 g 表；中間值與結果為 7, 12。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304105,"parameters":{"operation":"table_evaluate","A":[-8,-7,-6],"B":[-6,0,7],"C":[-9,0,12],"F":[[-8,0],[-7,7],[-6,-6]],"G":[[-6,0],[0,-9],[7,12]],"x":-7,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-8,-7,-6],\"B\":[-6,0,7],\"C\":[-9,0,12],\"F\":[[-8,0],[-7,7],[-6,-6]],\"G\":[[-6,0],[0,-9],[7,12]],\"operation\":\"table_evaluate\",\"x\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0006","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-7, -6, -5}、B={-7, 0, 8}、C={-11, 0, 14}；f 表=[(-7, 8), (-6, -7), (-5, 0)]，g 表=[(-7, 14), (0, 0), (8, -11)]。求 (g∘f)(-5)。","answer":{"kind":"short_text","value":"0","explanation_zh":"先取 f(-5)，再以其中間值查 g 表；中間值與結果為 0, 0。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304106,"parameters":{"operation":"table_evaluate","A":[-7,-6,-5],"B":[-7,0,8],"C":[-11,0,14],"F":[[-7,8],[-6,-7],[-5,0]],"G":[[-7,14],[0,0],[8,-11]],"x":-5,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-7,-6,-5],\"B\":[-7,0,8],\"C\":[-11,0,14],\"F\":[[-7,8],[-6,-7],[-5,0]],\"G\":[[-7,14],[0,0],[8,-11]],\"operation\":\"table_evaluate\",\"x\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0007","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-6, -5, -4}、B={-8, 0, 9}、C={-13, 0, 16}；f 表=[(-6, -8), (-5, 0), (-4, 9)]，g 表=[(-8, -13), (0, 16), (9, 0)]。求 (g∘f)(-6)。","answer":{"kind":"short_text","value":"-13","explanation_zh":"先取 f(-6)，再以其中間值查 g 表；中間值與結果為 -8, -13。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304107,"parameters":{"operation":"table_evaluate","A":[-6,-5,-4],"B":[-8,0,9],"C":[-13,0,16],"F":[[-6,-8],[-5,0],[-4,9]],"G":[[-8,-13],[0,16],[9,0]],"x":-6,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-6,-5,-4],\"B\":[-8,0,9],\"C\":[-13,0,16],\"F\":[[-6,-8],[-5,0],[-4,9]],\"G\":[[-8,-13],[0,16],[9,0]],\"operation\":\"table_evaluate\",\"x\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0008","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-5, -4, -3}、B={-9, 0, 10}、C={-15, 0, 18}；f 表=[(-5, 0), (-4, 10), (-3, -9)]，g 表=[(-9, 0), (0, -15), (10, 18)]。求 (g∘f)(-4)。","answer":{"kind":"short_text","value":"18","explanation_zh":"先取 f(-4)，再以其中間值查 g 表；中間值與結果為 10, 18。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304108,"parameters":{"operation":"table_evaluate","A":[-5,-4,-3],"B":[-9,0,10],"C":[-15,0,18],"F":[[-5,0],[-4,10],[-3,-9]],"G":[[-9,0],[0,-15],[10,18]],"x":-4,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-5,-4,-3],\"B\":[-9,0,10],\"C\":[-15,0,18],\"F\":[[-5,0],[-4,10],[-3,-9]],\"G\":[[-9,0],[0,-15],[10,18]],\"operation\":\"table_evaluate\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0009","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-4, -3, -2}、B={-10, 0, 11}、C={-17, 0, 20}；f 表=[(-4, 11), (-3, -10), (-2, 0)]，g 表=[(-10, 20), (0, 0), (11, -17)]。求 (g∘f)(-2)。","answer":{"kind":"short_text","value":"0","explanation_zh":"先取 f(-2)，再以其中間值查 g 表；中間值與結果為 0, 0。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304109,"parameters":{"operation":"table_evaluate","A":[-4,-3,-2],"B":[-10,0,11],"C":[-17,0,20],"F":[[-4,11],[-3,-10],[-2,0]],"G":[[-10,20],[0,0],[11,-17]],"x":-2,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-4,-3,-2],\"B\":[-10,0,11],\"C\":[-17,0,20],\"F\":[[-4,11],[-3,-10],[-2,0]],\"G\":[[-10,20],[0,0],[11,-17]],\"operation\":\"table_evaluate\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0010","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-3, -2, -1}、B={-11, 0, 12}、C={-19, 0, 22}；f 表=[(-3, -11), (-2, 0), (-1, 12)]，g 表=[(-11, -19), (0, 22), (12, 0)]。求 (g∘f)(-3)。","answer":{"kind":"short_text","value":"-19","explanation_zh":"先取 f(-3)，再以其中間值查 g 表；中間值與結果為 -11, -19。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304110,"parameters":{"operation":"table_evaluate","A":[-3,-2,-1],"B":[-11,0,12],"C":[-19,0,22],"F":[[-3,-11],[-2,0],[-1,12]],"G":[[-11,-19],[0,22],[12,0]],"x":-3,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-3,-2,-1],\"B\":[-11,0,12],\"C\":[-19,0,22],\"F\":[[-3,-11],[-2,0],[-1,12]],\"G\":[[-11,-19],[0,22],[12,0]],\"operation\":\"table_evaluate\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0011","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-2, -1, 0}、B={-12, 0, 13}、C={-21, 0, 24}；f 表=[(-2, 0), (-1, 13), (0, -12)]，g 表=[(-12, 0), (0, -21), (13, 24)]。求 (g∘f)(-1)。","answer":{"kind":"short_text","value":"24","explanation_zh":"先取 f(-1)，再以其中間值查 g 表；中間值與結果為 13, 24。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304111,"parameters":{"operation":"table_evaluate","A":[-2,-1,0],"B":[-12,0,13],"C":[-21,0,24],"F":[[-2,0],[-1,13],[0,-12]],"G":[[-12,0],[0,-21],[13,24]],"x":-1,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-2,-1,0],\"B\":[-12,0,13],\"C\":[-21,0,24],\"F\":[[-2,0],[-1,13],[0,-12]],\"G\":[[-12,0],[0,-21],[13,24]],\"operation\":\"table_evaluate\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0012","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={-1, 0, 1}、B={-13, 0, 14}、C={-23, 0, 26}；f 表=[(-1, 14), (0, -13), (1, 0)]，g 表=[(-13, 26), (0, 0), (14, -23)]。求 (g∘f)(1)。","answer":{"kind":"short_text","value":"0","explanation_zh":"先取 f(1)，再以其中間值查 g 表；中間值與結果為 0, 0。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304112,"parameters":{"operation":"table_evaluate","A":[-1,0,1],"B":[-13,0,14],"C":[-23,0,26],"F":[[-1,14],[0,-13],[1,0]],"G":[[-13,26],[0,0],[14,-23]],"x":1,"semantic_template":"qf-composition-table-evaluation/{\"A\":[-1,0,1],\"B\":[-13,0,14],\"C\":[-23,0,26],\"F\":[[-1,14],[0,-13],[1,0]],\"G\":[[-13,26],[0,0],[14,-23]],\"operation\":\"table_evaluate\",\"x\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0013","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={0, 1, 2}、B={-14, 0, 15}、C={-25, 0, 28}；f 表=[(0, -14), (1, 0), (2, 15)]，g 表=[(-14, -25), (0, 28), (15, 0)]。求 (g∘f)(0)。","answer":{"kind":"short_text","value":"-25","explanation_zh":"先取 f(0)，再以其中間值查 g 表；中間值與結果為 -14, -25。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304113,"parameters":{"operation":"table_evaluate","A":[0,1,2],"B":[-14,0,15],"C":[-25,0,28],"F":[[0,-14],[1,0],[2,15]],"G":[[-14,-25],[0,28],[15,0]],"x":0,"semantic_template":"qf-composition-table-evaluation/{\"A\":[0,1,2],\"B\":[-14,0,15],\"C\":[-25,0,28],\"F\":[[0,-14],[1,0],[2,15]],\"G\":[[-14,-25],[0,28],[15,0]],\"operation\":\"table_evaluate\",\"x\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0014","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={1, 2, 3}、B={-15, 0, 16}、C={-27, 0, 30}；f 表=[(1, 0), (2, 16), (3, -15)]，g 表=[(-15, 0), (0, -27), (16, 30)]。求 (g∘f)(2)。","answer":{"kind":"short_text","value":"30","explanation_zh":"先取 f(2)，再以其中間值查 g 表；中間值與結果為 16, 30。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304114,"parameters":{"operation":"table_evaluate","A":[1,2,3],"B":[-15,0,16],"C":[-27,0,30],"F":[[1,0],[2,16],[3,-15]],"G":[[-15,0],[0,-27],[16,30]],"x":2,"semantic_template":"qf-composition-table-evaluation/{\"A\":[1,2,3],\"B\":[-15,0,16],\"C\":[-27,0,30],\"F\":[[1,0],[2,16],[3,-15]],\"G\":[[-15,0],[0,-27],[16,30]],\"operation\":\"table_evaluate\",\"x\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0015","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={2, 3, 4}、B={-16, 0, 17}、C={-29, 0, 32}；f 表=[(2, 17), (3, -16), (4, 0)]，g 表=[(-16, 32), (0, 0), (17, -29)]。求 (g∘f)(4)。","answer":{"kind":"short_text","value":"0","explanation_zh":"先取 f(4)，再以其中間值查 g 表；中間值與結果為 0, 0。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304115,"parameters":{"operation":"table_evaluate","A":[2,3,4],"B":[-16,0,17],"C":[-29,0,32],"F":[[2,17],[3,-16],[4,0]],"G":[[-16,32],[0,0],[17,-29]],"x":4,"semantic_template":"qf-composition-table-evaluation/{\"A\":[2,3,4],\"B\":[-16,0,17],\"C\":[-29,0,32],\"F\":[[2,17],[3,-16],[4,0]],\"G\":[[-16,32],[0,0],[17,-29]],\"operation\":\"table_evaluate\",\"x\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0016","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={3, 4, 5}、B={-17, 0, 18}、C={-31, 0, 34}；f 表=[(3, -17), (4, 0), (5, 18)]，g 表=[(-17, -31), (0, 34), (18, 0)]。求 (g∘f)(3)。","answer":{"kind":"short_text","value":"-31","explanation_zh":"先取 f(3)，再以其中間值查 g 表；中間值與結果為 -17, -31。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304116,"parameters":{"operation":"table_evaluate","A":[3,4,5],"B":[-17,0,18],"C":[-31,0,34],"F":[[3,-17],[4,0],[5,18]],"G":[[-17,-31],[0,34],[18,0]],"x":3,"semantic_template":"qf-composition-table-evaluation/{\"A\":[3,4,5],\"B\":[-17,0,18],\"C\":[-31,0,34],\"F\":[[3,-17],[4,0],[5,18]],\"G\":[[-17,-31],[0,34],[18,0]],\"operation\":\"table_evaluate\",\"x\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0017","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={4, 5, 6}、B={-18, 0, 19}、C={-33, 0, 36}；f 表=[(4, 0), (5, 19), (6, -18)]，g 表=[(-18, 0), (0, -33), (19, 36)]。求 (g∘f)(5)。","answer":{"kind":"short_text","value":"36","explanation_zh":"先取 f(5)，再以其中間值查 g 表；中間值與結果為 19, 36。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304117,"parameters":{"operation":"table_evaluate","A":[4,5,6],"B":[-18,0,19],"C":[-33,0,36],"F":[[4,0],[5,19],[6,-18]],"G":[[-18,0],[0,-33],[19,36]],"x":5,"semantic_template":"qf-composition-table-evaluation/{\"A\":[4,5,6],\"B\":[-18,0,19],\"C\":[-33,0,36],\"F\":[[4,0],[5,19],[6,-18]],\"G\":[[-18,0],[0,-33],[19,36]],\"operation\":\"table_evaluate\",\"x\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0018","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={5, 6, 7}、B={-19, 0, 20}、C={-35, 0, 38}；f 表=[(5, 20), (6, -19), (7, 0)]，g 表=[(-19, 38), (0, 0), (20, -35)]。求 (g∘f)(7)。","answer":{"kind":"short_text","value":"0","explanation_zh":"先取 f(7)，再以其中間值查 g 表；中間值與結果為 0, 0。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304118,"parameters":{"operation":"table_evaluate","A":[5,6,7],"B":[-19,0,20],"C":[-35,0,38],"F":[[5,20],[6,-19],[7,0]],"G":[[-19,38],[0,0],[20,-35]],"x":7,"semantic_template":"qf-composition-table-evaluation/{\"A\":[5,6,7],\"B\":[-19,0,20],\"C\":[-35,0,38],\"F\":[[5,20],[6,-19],[7,0]],\"G\":[[-19,38],[0,0],[20,-35]],\"operation\":\"table_evaluate\",\"x\":7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0019","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={6, 7, 8}、B={-20, 0, 21}、C={-37, 0, 40}；f 表=[(6, -20), (7, 0), (8, 21)]，g 表=[(-20, -37), (0, 40), (21, 0)]。求 (g∘f)(6)。","answer":{"kind":"short_text","value":"-37","explanation_zh":"先取 f(6)，再以其中間值查 g 表；中間值與結果為 -20, -37。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304119,"parameters":{"operation":"table_evaluate","A":[6,7,8],"B":[-20,0,21],"C":[-37,0,40],"F":[[6,-20],[7,0],[8,21]],"G":[[-20,-37],[0,40],[21,0]],"x":6,"semantic_template":"qf-composition-table-evaluation/{\"A\":[6,7,8],\"B\":[-20,0,21],\"C\":[-37,0,40],\"F\":[[6,-20],[7,0],[8,21]],\"G\":[[-20,-37],[0,40],[21,0]],\"operation\":\"table_evaluate\",\"x\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0020","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={7, 8, 9}、B={-21, 0, 22}、C={-39, 0, 42}；f 表=[(7, 0), (8, 22), (9, -21)]，g 表=[(-21, 0), (0, -39), (22, 42)]。求 (g∘f)(8)。","answer":{"kind":"short_text","value":"42","explanation_zh":"先取 f(8)，再以其中間值查 g 表；中間值與結果為 22, 42。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304120,"parameters":{"operation":"table_evaluate","A":[7,8,9],"B":[-21,0,22],"C":[-39,0,42],"F":[[7,0],[8,22],[9,-21]],"G":[[-21,0],[0,-39],[22,42]],"x":8,"semantic_template":"qf-composition-table-evaluation/{\"A\":[7,8,9],\"B\":[-21,0,22],\"C\":[-39,0,42],\"F\":[[7,0],[8,22],[9,-21]],\"G\":[[-21,0],[0,-39],[22,42]],\"operation\":\"table_evaluate\",\"x\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0021","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={8, 9, 10}、B={-22, 0, 23}、C={-41, 0, 44}；f 表=[(8, 23), (9, -22), (10, 0)]，g 表=[(-22, 44), (0, 0), (23, -41)]。求 (g∘f)(10)。","answer":{"kind":"short_text","value":"0","explanation_zh":"先取 f(10)，再以其中間值查 g 表；中間值與結果為 0, 0。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304121,"parameters":{"operation":"table_evaluate","A":[8,9,10],"B":[-22,0,23],"C":[-41,0,44],"F":[[8,23],[9,-22],[10,0]],"G":[[-22,44],[0,0],[23,-41]],"x":10,"semantic_template":"qf-composition-table-evaluation/{\"A\":[8,9,10],\"B\":[-22,0,23],\"C\":[-41,0,44],\"F\":[[8,23],[9,-22],[10,0]],\"G\":[[-22,44],[0,0],[23,-41]],\"operation\":\"table_evaluate\",\"x\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0022","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={9, 10, 11}、B={-23, 0, 24}、C={-43, 0, 46}；f 表=[(9, -23), (10, 0), (11, 24)]，g 表=[(-23, -43), (0, 46), (24, 0)]。求 (g∘f)(9)。","answer":{"kind":"short_text","value":"-43","explanation_zh":"先取 f(9)，再以其中間值查 g 表；中間值與結果為 -23, -43。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304122,"parameters":{"operation":"table_evaluate","A":[9,10,11],"B":[-23,0,24],"C":[-43,0,46],"F":[[9,-23],[10,0],[11,24]],"G":[[-23,-43],[0,46],[24,0]],"x":9,"semantic_template":"qf-composition-table-evaluation/{\"A\":[9,10,11],\"B\":[-23,0,24],\"C\":[-43,0,46],\"F\":[[9,-23],[10,0],[11,24]],\"G\":[[-23,-43],[0,46],[24,0]],\"operation\":\"table_evaluate\",\"x\":9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0023","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={10, 11, 12}、B={-24, 0, 25}、C={-45, 0, 48}；f 表=[(10, 0), (11, 25), (12, -24)]，g 表=[(-24, 0), (0, -45), (25, 48)]。求 (g∘f)(11)。","answer":{"kind":"short_text","value":"48","explanation_zh":"先取 f(11)，再以其中間值查 g 表；中間值與結果為 25, 48。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304123,"parameters":{"operation":"table_evaluate","A":[10,11,12],"B":[-24,0,25],"C":[-45,0,48],"F":[[10,0],[11,25],[12,-24]],"G":[[-24,0],[0,-45],[25,48]],"x":11,"semantic_template":"qf-composition-table-evaluation/{\"A\":[10,11,12],\"B\":[-24,0,25],\"C\":[-45,0,48],\"F\":[[10,0],[11,25],[12,-24]],\"G\":[[-24,0],[0,-45],[25,48]],\"operation\":\"table_evaluate\",\"x\":11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0024","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={11, 12, 13}、B={-25, 0, 26}、C={-47, 0, 50}；f 表=[(11, 26), (12, -25), (13, 0)]，g 表=[(-25, 50), (0, 0), (26, -47)]。求 (g∘f)(13)。","answer":{"kind":"short_text","value":"0","explanation_zh":"先取 f(13)，再以其中間值查 g 表；中間值與結果為 0, 0。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304124,"parameters":{"operation":"table_evaluate","A":[11,12,13],"B":[-25,0,26],"C":[-47,0,50],"F":[[11,26],[12,-25],[13,0]],"G":[[-25,50],[0,0],[26,-47]],"x":13,"semantic_template":"qf-composition-table-evaluation/{\"A\":[11,12,13],\"B\":[-25,0,26],\"C\":[-47,0,50],\"F\":[[11,26],[12,-25],[13,0]],\"G\":[[-25,50],[0,0],[26,-47]],\"operation\":\"table_evaluate\",\"x\":13}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-table-evaluation-0025","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"有限函數表的合成值","stem_zh":"明示總函數 f:A→B、g:B→C，A={12, 13, 14}、B={-26, 0, 27}、C={-49, 0, 52}；f 表=[(12, -26), (13, 0), (14, 27)]，g 表=[(-26, -49), (0, 52), (27, 0)]。求 (g∘f)(12)。","answer":{"kind":"short_text","value":"-49","explanation_zh":"先取 f(12)，再以其中間值查 g 表；中間值與結果為 -26, -49。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值","總函數合成"]},"variant":{"family_id":"qf-composition-table-evaluation","seed":202609304125,"parameters":{"operation":"table_evaluate","A":[12,13,14],"B":[-26,0,27],"C":[-49,0,52],"F":[[12,-26],[13,0],[14,27]],"G":[[-26,-49],[0,52],[27,0]],"x":12,"semantic_template":"qf-composition-table-evaluation/{\"A\":[12,13,14],\"B\":[-26,0,27],\"C\":[-49,0,52],\"F\":[[12,-26],[13,0],[14,27]],\"G\":[[-26,-49],[0,52],[27,0]],\"operation\":\"table_evaluate\",\"x\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0001","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A=∅、B={0}、D=∅、C=∅；f 表=[]，g 表=[]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"∅","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 ∅。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304201,"parameters":{"operation":"restricted_domain","A":[],"B":[0],"D":[],"C":[],"F":[],"G":[],"semantic_template":"qf-composition-domain-set/{\"A\":[],\"B\":[0],\"C\":[],\"D\":[],\"F\":[],\"G\":[],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0002","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-1, 0, 1}、B={-2, 0, 2}、D=∅、C={5}；f 表=[(-1, -2), (0, 0), (1, 2)]，g 表=[]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"∅","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 ∅。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304202,"parameters":{"operation":"restricted_domain","A":[-1,0,1],"B":[-2,0,2],"D":[],"C":[5],"F":[[-1,-2],[0,0],[1,2]],"G":[],"semantic_template":"qf-composition-domain-set/{\"A\":[-1,0,1],\"B\":[-2,0,2],\"C\":[5],\"D\":[],\"F\":[[-1,-2],[0,0],[1,2]],\"G\":[],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0003","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-10, -9, -8}、B={-4, 0, 5}、D={-4, 0}、C={-4, 1, 5}；f 表=[(-10, 5), (-9, -4), (-8, 0)]，g 表=[(-4, 5), (0, -4)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{-9, -8}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {-9, -8}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304203,"parameters":{"operation":"restricted_domain","A":[-10,-9,-8],"B":[-4,0,5],"D":[-4,0],"C":[-4,1,5],"F":[[-10,5],[-9,-4],[-8,0]],"G":[[-4,5],[0,-4]],"semantic_template":"qf-composition-domain-set/{\"A\":[-10,-9,-8],\"B\":[-4,0,5],\"C\":[-4,1,5],\"D\":[-4,0],\"F\":[[-10,5],[-9,-4],[-8,0]],\"G\":[[-4,5],[0,-4]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0004","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-9, -8, -7}、B={-5, 0, 6}、D={102}、C={-6, 1, 7}；f 表=[(-9, -5), (-8, 0), (-7, 6)]，g 表=[(102, -6)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"∅","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 ∅。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304204,"parameters":{"operation":"restricted_domain","A":[-9,-8,-7],"B":[-5,0,6],"D":[102],"C":[-6,1,7],"F":[[-9,-5],[-8,0],[-7,6]],"G":[[102,-6]],"semantic_template":"qf-composition-domain-set/{\"A\":[-9,-8,-7],\"B\":[-5,0,6],\"C\":[-6,1,7],\"D\":[102],\"F\":[[-9,-5],[-8,0],[-7,6]],\"G\":[[102,-6]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0005","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-8, -7, -6}、B={-6, 0, 7}、D={-6, 0, 7}、C={-8, 1, 9}；f 表=[(-8, 0), (-7, 7), (-6, -6)]，g 表=[(-6, 1), (0, 9), (7, -8)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{-8, -7, -6}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {-8, -7, -6}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304205,"parameters":{"operation":"restricted_domain","A":[-8,-7,-6],"B":[-6,0,7],"D":[-6,0,7],"C":[-8,1,9],"F":[[-8,0],[-7,7],[-6,-6]],"G":[[-6,1],[0,9],[7,-8]],"semantic_template":"qf-composition-domain-set/{\"A\":[-8,-7,-6],\"B\":[-6,0,7],\"C\":[-8,1,9],\"D\":[-6,0,7],\"F\":[[-8,0],[-7,7],[-6,-6]],\"G\":[[-6,1],[0,9],[7,-8]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0006","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-7, -6, -5}、B={-7, 0, 8}、D={0}、C={-10, 1, 11}；f 表=[(-7, 8), (-6, -7), (-5, 0)]，g 表=[(0, 11)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{-5}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {-5}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304206,"parameters":{"operation":"restricted_domain","A":[-7,-6,-5],"B":[-7,0,8],"D":[0],"C":[-10,1,11],"F":[[-7,8],[-6,-7],[-5,0]],"G":[[0,11]],"semantic_template":"qf-composition-domain-set/{\"A\":[-7,-6,-5],\"B\":[-7,0,8],\"C\":[-10,1,11],\"D\":[0],\"F\":[[-7,8],[-6,-7],[-5,0]],\"G\":[[0,11]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0007","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-6, -5, -4}、B={-8, 0, 9}、D={-8, 0}、C={-12, 1, 13}；f 表=[(-6, -8), (-5, 0), (-4, 9)]，g 表=[(-8, -12), (0, 1)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{-6, -5}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {-6, -5}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304207,"parameters":{"operation":"restricted_domain","A":[-6,-5,-4],"B":[-8,0,9],"D":[-8,0],"C":[-12,1,13],"F":[[-6,-8],[-5,0],[-4,9]],"G":[[-8,-12],[0,1]],"semantic_template":"qf-composition-domain-set/{\"A\":[-6,-5,-4],\"B\":[-8,0,9],\"C\":[-12,1,13],\"D\":[-8,0],\"F\":[[-6,-8],[-5,0],[-4,9]],\"G\":[[-8,-12],[0,1]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0008","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-5, -4, -3}、B={-9, 0, 10}、D={106}、C={-14, 1, 15}；f 表=[(-5, 0), (-4, 10), (-3, -9)]，g 表=[(106, 1)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"∅","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 ∅。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304208,"parameters":{"operation":"restricted_domain","A":[-5,-4,-3],"B":[-9,0,10],"D":[106],"C":[-14,1,15],"F":[[-5,0],[-4,10],[-3,-9]],"G":[[106,1]],"semantic_template":"qf-composition-domain-set/{\"A\":[-5,-4,-3],\"B\":[-9,0,10],\"C\":[-14,1,15],\"D\":[106],\"F\":[[-5,0],[-4,10],[-3,-9]],\"G\":[[106,1]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0009","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-4, -3, -2}、B={-10, 0, 11}、D={-10, 0, 11}、C={-16, 1, 17}；f 表=[(-4, 11), (-3, -10), (-2, 0)]，g 表=[(-10, 17), (0, -16), (11, 1)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{-4, -3, -2}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {-4, -3, -2}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304209,"parameters":{"operation":"restricted_domain","A":[-4,-3,-2],"B":[-10,0,11],"D":[-10,0,11],"C":[-16,1,17],"F":[[-4,11],[-3,-10],[-2,0]],"G":[[-10,17],[0,-16],[11,1]],"semantic_template":"qf-composition-domain-set/{\"A\":[-4,-3,-2],\"B\":[-10,0,11],\"C\":[-16,1,17],\"D\":[-10,0,11],\"F\":[[-4,11],[-3,-10],[-2,0]],\"G\":[[-10,17],[0,-16],[11,1]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0010","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-3, -2, -1}、B={-11, 0, 12}、D={0}、C={-18, 1, 19}；f 表=[(-3, -11), (-2, 0), (-1, 12)]，g 表=[(0, -18)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{-2}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {-2}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304210,"parameters":{"operation":"restricted_domain","A":[-3,-2,-1],"B":[-11,0,12],"D":[0],"C":[-18,1,19],"F":[[-3,-11],[-2,0],[-1,12]],"G":[[0,-18]],"semantic_template":"qf-composition-domain-set/{\"A\":[-3,-2,-1],\"B\":[-11,0,12],\"C\":[-18,1,19],\"D\":[0],\"F\":[[-3,-11],[-2,0],[-1,12]],\"G\":[[0,-18]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0011","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-2, -1, 0}、B={-12, 0, 13}、D={-12, 0}、C={-20, 1, 21}；f 表=[(-2, 0), (-1, 13), (0, -12)]，g 表=[(-12, 1), (0, 21)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{-2, 0}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {-2, 0}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304211,"parameters":{"operation":"restricted_domain","A":[-2,-1,0],"B":[-12,0,13],"D":[-12,0],"C":[-20,1,21],"F":[[-2,0],[-1,13],[0,-12]],"G":[[-12,1],[0,21]],"semantic_template":"qf-composition-domain-set/{\"A\":[-2,-1,0],\"B\":[-12,0,13],\"C\":[-20,1,21],\"D\":[-12,0],\"F\":[[-2,0],[-1,13],[0,-12]],\"G\":[[-12,1],[0,21]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0012","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={-1, 0, 1}、B={-13, 0, 14}、D={110}、C={-22, 1, 23}；f 表=[(-1, 14), (0, -13), (1, 0)]，g 表=[(110, 23)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"∅","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 ∅。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304212,"parameters":{"operation":"restricted_domain","A":[-1,0,1],"B":[-13,0,14],"D":[110],"C":[-22,1,23],"F":[[-1,14],[0,-13],[1,0]],"G":[[110,23]],"semantic_template":"qf-composition-domain-set/{\"A\":[-1,0,1],\"B\":[-13,0,14],\"C\":[-22,1,23],\"D\":[110],\"F\":[[-1,14],[0,-13],[1,0]],\"G\":[[110,23]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0013","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={0, 1, 2}、B={-14, 0, 15}、D={-14, 0, 15}、C={-24, 1, 25}；f 表=[(0, -14), (1, 0), (2, 15)]，g 表=[(-14, -24), (0, 1), (15, 25)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{0, 1, 2}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {0, 1, 2}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304213,"parameters":{"operation":"restricted_domain","A":[0,1,2],"B":[-14,0,15],"D":[-14,0,15],"C":[-24,1,25],"F":[[0,-14],[1,0],[2,15]],"G":[[-14,-24],[0,1],[15,25]],"semantic_template":"qf-composition-domain-set/{\"A\":[0,1,2],\"B\":[-14,0,15],\"C\":[-24,1,25],\"D\":[-14,0,15],\"F\":[[0,-14],[1,0],[2,15]],\"G\":[[-14,-24],[0,1],[15,25]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0014","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={1, 2, 3}、B={-15, 0, 16}、D={0}、C={-26, 1, 27}；f 表=[(1, 0), (2, 16), (3, -15)]，g 表=[(0, 1)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{1}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {1}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304214,"parameters":{"operation":"restricted_domain","A":[1,2,3],"B":[-15,0,16],"D":[0],"C":[-26,1,27],"F":[[1,0],[2,16],[3,-15]],"G":[[0,1]],"semantic_template":"qf-composition-domain-set/{\"A\":[1,2,3],\"B\":[-15,0,16],\"C\":[-26,1,27],\"D\":[0],\"F\":[[1,0],[2,16],[3,-15]],\"G\":[[0,1]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0015","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={2, 3, 4}、B={-16, 0, 17}、D={-16, 0}、C={-28, 1, 29}；f 表=[(2, 17), (3, -16), (4, 0)]，g 表=[(-16, 29), (0, -28)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{3, 4}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {3, 4}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304215,"parameters":{"operation":"restricted_domain","A":[2,3,4],"B":[-16,0,17],"D":[-16,0],"C":[-28,1,29],"F":[[2,17],[3,-16],[4,0]],"G":[[-16,29],[0,-28]],"semantic_template":"qf-composition-domain-set/{\"A\":[2,3,4],\"B\":[-16,0,17],\"C\":[-28,1,29],\"D\":[-16,0],\"F\":[[2,17],[3,-16],[4,0]],\"G\":[[-16,29],[0,-28]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0016","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={3, 4, 5}、B={-17, 0, 18}、D={114}、C={-30, 1, 31}；f 表=[(3, -17), (4, 0), (5, 18)]，g 表=[(114, -30)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"∅","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 ∅。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304216,"parameters":{"operation":"restricted_domain","A":[3,4,5],"B":[-17,0,18],"D":[114],"C":[-30,1,31],"F":[[3,-17],[4,0],[5,18]],"G":[[114,-30]],"semantic_template":"qf-composition-domain-set/{\"A\":[3,4,5],\"B\":[-17,0,18],\"C\":[-30,1,31],\"D\":[114],\"F\":[[3,-17],[4,0],[5,18]],\"G\":[[114,-30]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0017","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={4, 5, 6}、B={-18, 0, 19}、D={-18, 0, 19}、C={-32, 1, 33}；f 表=[(4, 0), (5, 19), (6, -18)]，g 表=[(-18, 1), (0, 33), (19, -32)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{4, 5, 6}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {4, 5, 6}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304217,"parameters":{"operation":"restricted_domain","A":[4,5,6],"B":[-18,0,19],"D":[-18,0,19],"C":[-32,1,33],"F":[[4,0],[5,19],[6,-18]],"G":[[-18,1],[0,33],[19,-32]],"semantic_template":"qf-composition-domain-set/{\"A\":[4,5,6],\"B\":[-18,0,19],\"C\":[-32,1,33],\"D\":[-18,0,19],\"F\":[[4,0],[5,19],[6,-18]],\"G\":[[-18,1],[0,33],[19,-32]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0018","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={5, 6, 7}、B={-19, 0, 20}、D={0}、C={-34, 1, 35}；f 表=[(5, 20), (6, -19), (7, 0)]，g 表=[(0, 35)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{7}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {7}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304218,"parameters":{"operation":"restricted_domain","A":[5,6,7],"B":[-19,0,20],"D":[0],"C":[-34,1,35],"F":[[5,20],[6,-19],[7,0]],"G":[[0,35]],"semantic_template":"qf-composition-domain-set/{\"A\":[5,6,7],\"B\":[-19,0,20],\"C\":[-34,1,35],\"D\":[0],\"F\":[[5,20],[6,-19],[7,0]],\"G\":[[0,35]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0019","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={6, 7, 8}、B={-20, 0, 21}、D={-20, 0}、C={-36, 1, 37}；f 表=[(6, -20), (7, 0), (8, 21)]，g 表=[(-20, -36), (0, 1)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{6, 7}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {6, 7}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304219,"parameters":{"operation":"restricted_domain","A":[6,7,8],"B":[-20,0,21],"D":[-20,0],"C":[-36,1,37],"F":[[6,-20],[7,0],[8,21]],"G":[[-20,-36],[0,1]],"semantic_template":"qf-composition-domain-set/{\"A\":[6,7,8],\"B\":[-20,0,21],\"C\":[-36,1,37],\"D\":[-20,0],\"F\":[[6,-20],[7,0],[8,21]],\"G\":[[-20,-36],[0,1]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0020","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={7, 8, 9}、B={-21, 0, 22}、D={118}、C={-38, 1, 39}；f 表=[(7, 0), (8, 22), (9, -21)]，g 表=[(118, 1)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"∅","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 ∅。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304220,"parameters":{"operation":"restricted_domain","A":[7,8,9],"B":[-21,0,22],"D":[118],"C":[-38,1,39],"F":[[7,0],[8,22],[9,-21]],"G":[[118,1]],"semantic_template":"qf-composition-domain-set/{\"A\":[7,8,9],\"B\":[-21,0,22],\"C\":[-38,1,39],\"D\":[118],\"F\":[[7,0],[8,22],[9,-21]],\"G\":[[118,1]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0021","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={8, 9, 10}、B={-22, 0, 23}、D={-22, 0, 23}、C={-40, 1, 41}；f 表=[(8, 23), (9, -22), (10, 0)]，g 表=[(-22, 41), (0, -40), (23, 1)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{8, 9, 10}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {8, 9, 10}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304221,"parameters":{"operation":"restricted_domain","A":[8,9,10],"B":[-22,0,23],"D":[-22,0,23],"C":[-40,1,41],"F":[[8,23],[9,-22],[10,0]],"G":[[-22,41],[0,-40],[23,1]],"semantic_template":"qf-composition-domain-set/{\"A\":[8,9,10],\"B\":[-22,0,23],\"C\":[-40,1,41],\"D\":[-22,0,23],\"F\":[[8,23],[9,-22],[10,0]],\"G\":[[-22,41],[0,-40],[23,1]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0022","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={9, 10, 11}、B={-23, 0, 24}、D={0}、C={-42, 1, 43}；f 表=[(9, -23), (10, 0), (11, 24)]，g 表=[(0, -42)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{10}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {10}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304222,"parameters":{"operation":"restricted_domain","A":[9,10,11],"B":[-23,0,24],"D":[0],"C":[-42,1,43],"F":[[9,-23],[10,0],[11,24]],"G":[[0,-42]],"semantic_template":"qf-composition-domain-set/{\"A\":[9,10,11],\"B\":[-23,0,24],\"C\":[-42,1,43],\"D\":[0],\"F\":[[9,-23],[10,0],[11,24]],\"G\":[[0,-42]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0023","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={10, 11, 12}、B={-24, 0, 25}、D={-24, 0}、C={-44, 1, 45}；f 表=[(10, 0), (11, 25), (12, -24)]，g 表=[(-24, 1), (0, 45)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{10, 12}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {10, 12}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304223,"parameters":{"operation":"restricted_domain","A":[10,11,12],"B":[-24,0,25],"D":[-24,0],"C":[-44,1,45],"F":[[10,0],[11,25],[12,-24]],"G":[[-24,1],[0,45]],"semantic_template":"qf-composition-domain-set/{\"A\":[10,11,12],\"B\":[-24,0,25],\"C\":[-44,1,45],\"D\":[-24,0],\"F\":[[10,0],[11,25],[12,-24]],\"G\":[[-24,1],[0,45]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0024","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={11, 12, 13}、B={-25, 0, 26}、D={122}、C={-46, 1, 47}；f 表=[(11, 26), (12, -25), (13, 0)]，g 表=[(122, 47)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"∅","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 ∅。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304224,"parameters":{"operation":"restricted_domain","A":[11,12,13],"B":[-25,0,26],"D":[122],"C":[-46,1,47],"F":[[11,26],[12,-25],[13,0]],"G":[[122,47]],"semantic_template":"qf-composition-domain-set/{\"A\":[11,12,13],\"B\":[-25,0,26],\"C\":[-46,1,47],\"D\":[122],\"F\":[[11,26],[12,-25],[13,0]],\"G\":[[122,47]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-domain-set-0025","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"受限合成定義域","stem_zh":"明示總函數 f:A→B 與 g:D→C；A={12, 13, 14}、B={-26, 0, 27}、D={-26, 0, 27}、C={-48, 1, 49}；f 表=[(12, -26), (13, 0), (14, 27)]，g 表=[(-26, -48), (0, 1), (27, 49)]。列出受限合成的允許輸入集合 {x∈A:f(x)∈D}。","answer":{"kind":"short_text","value":"{12, 13, 14}","explanation_zh":"逐個檢查 A 中輸入的 f 值是否落入 D；保留下來的集合為 {12, 13, 14}。沒有相容中間值時就是空集合。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["中間值相容","空集合邊界"]},"variant":{"family_id":"qf-composition-domain-set","seed":202609304225,"parameters":{"operation":"restricted_domain","A":[12,13,14],"B":[-26,0,27],"D":[-26,0,27],"C":[-48,1,49],"F":[[12,-26],[13,0],[14,27]],"G":[[-26,-48],[0,1],[27,49]],"semantic_template":"qf-composition-domain-set/{\"A\":[12,13,14],\"B\":[-26,0,27],\"C\":[-48,1,49],\"D\":[-26,0,27],\"F\":[[12,-26],[13,0],[14,27]],\"G\":[[-26,-48],[0,1],[27,49]],\"operation\":\"restricted_domain\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0001","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(-12)；g:R→R，g(t)=(1)t+(6)。在 x=-12 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"是","explanation_zh":"兩種順序的值分別為 -18, -18；所以答案為是。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304301,"parameters":{"operation":"compare_at_input","a":1,"b":-12,"c":1,"d":6,"x":-12,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-12,\"c\":1,\"d\":6,\"operation\":\"compare_at_input\",\"x\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0002","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-2)t+(-11)；g:R→R，g(t)=(-1)t+(5)。在 x=-11 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -6, -43；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304302,"parameters":{"operation":"compare_at_input","a":-2,"b":-11,"c":-1,"d":5,"x":-11,"semantic_template":"qf-composition-order-comparison/{\"a\":-2,\"b\":-11,\"c\":-1,\"d\":5,\"operation\":\"compare_at_input\",\"x\":-11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0003","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-1)t+(-10)；g:R→R，g(t)=(0)t+(4)。在 x=-10 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 4, -14；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304303,"parameters":{"operation":"compare_at_input","a":-1,"b":-10,"c":0,"d":4,"x":-10,"semantic_template":"qf-composition-order-comparison/{\"a\":-1,\"b\":-10,\"c\":0,\"d\":4,\"operation\":\"compare_at_input\",\"x\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0004","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(0)t+(-9)；g:R→R，g(t)=(1)t+(3)。在 x=-9 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -6, -9；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304304,"parameters":{"operation":"compare_at_input","a":0,"b":-9,"c":1,"d":3,"x":-9,"semantic_template":"qf-composition-order-comparison/{\"a\":0,\"b\":-9,\"c\":1,\"d\":3,\"operation\":\"compare_at_input\",\"x\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0005","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(-8)；g:R→R，g(t)=(2)t+(2)。在 x=-8 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -30, -22；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304305,"parameters":{"operation":"compare_at_input","a":1,"b":-8,"c":2,"d":2,"x":-8,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-8,\"c\":2,\"d\":2,\"operation\":\"compare_at_input\",\"x\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0006","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(-7)；g:R→R，g(t)=(1)t+(1)。在 x=-7 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"是","explanation_zh":"兩種順序的值分別為 -13, -13；所以答案為是。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304306,"parameters":{"operation":"compare_at_input","a":1,"b":-7,"c":1,"d":1,"x":-7,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-7,\"c\":1,\"d\":1,\"operation\":\"compare_at_input\",\"x\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0007","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(3)t+(-6)；g:R→R，g(t)=(-1)t+(0)。在 x=-6 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 24, 12；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304307,"parameters":{"operation":"compare_at_input","a":3,"b":-6,"c":-1,"d":0,"x":-6,"semantic_template":"qf-composition-order-comparison/{\"a\":3,\"b\":-6,\"c\":-1,\"d\":0,\"operation\":\"compare_at_input\",\"x\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0008","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-3)t+(-5)；g:R→R，g(t)=(0)t+(-1)。在 x=-5 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -1, -2；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304308,"parameters":{"operation":"compare_at_input","a":-3,"b":-5,"c":0,"d":-1,"x":-5,"semantic_template":"qf-composition-order-comparison/{\"a\":-3,\"b\":-5,\"c\":0,\"d\":-1,\"operation\":\"compare_at_input\",\"x\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0009","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-2)t+(-4)；g:R→R，g(t)=(1)t+(-2)。在 x=-4 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 2, 8；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304309,"parameters":{"operation":"compare_at_input","a":-2,"b":-4,"c":1,"d":-2,"x":-4,"semantic_template":"qf-composition-order-comparison/{\"a\":-2,\"b\":-4,\"c\":1,\"d\":-2,\"operation\":\"compare_at_input\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0010","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-1)t+(-3)；g:R→R，g(t)=(2)t+(-3)。在 x=-3 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -3, 6；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304310,"parameters":{"operation":"compare_at_input","a":-1,"b":-3,"c":2,"d":-3,"x":-3,"semantic_template":"qf-composition-order-comparison/{\"a\":-1,\"b\":-3,\"c\":2,\"d\":-3,\"operation\":\"compare_at_input\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0011","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(-2)；g:R→R，g(t)=(1)t+(-4)。在 x=-2 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"是","explanation_zh":"兩種順序的值分別為 -8, -8；所以答案為是。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304311,"parameters":{"operation":"compare_at_input","a":1,"b":-2,"c":1,"d":-4,"x":-2,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-2,\"c\":1,\"d\":-4,\"operation\":\"compare_at_input\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0012","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(-1)；g:R→R，g(t)=(-1)t+(-5)。在 x=-1 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -3, -5；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304312,"parameters":{"operation":"compare_at_input","a":1,"b":-1,"c":-1,"d":-5,"x":-1,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-1,\"c\":-1,\"d\":-5,\"operation\":\"compare_at_input\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0013","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(2)t+(0)；g:R→R，g(t)=(0)t+(-6)。在 x=0 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -6, -12；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304313,"parameters":{"operation":"compare_at_input","a":2,"b":0,"c":0,"d":-6,"x":0,"semantic_template":"qf-composition-order-comparison/{\"a\":2,\"b\":0,\"c\":0,\"d\":-6,\"operation\":\"compare_at_input\",\"x\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0014","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(3)t+(1)；g:R→R，g(t)=(1)t+(6)。在 x=1 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 10, 22；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304314,"parameters":{"operation":"compare_at_input","a":3,"b":1,"c":1,"d":6,"x":1,"semantic_template":"qf-composition-order-comparison/{\"a\":3,\"b\":1,\"c\":1,\"d\":6,\"operation\":\"compare_at_input\",\"x\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0015","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-3)t+(2)；g:R→R，g(t)=(2)t+(5)。在 x=2 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -3, -25；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304315,"parameters":{"operation":"compare_at_input","a":-3,"b":2,"c":2,"d":5,"x":2,"semantic_template":"qf-composition-order-comparison/{\"a\":-3,\"b\":2,\"c\":2,\"d\":5,\"operation\":\"compare_at_input\",\"x\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0016","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(3)；g:R→R，g(t)=(1)t+(4)。在 x=3 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"是","explanation_zh":"兩種順序的值分別為 10, 10；所以答案為是。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304316,"parameters":{"operation":"compare_at_input","a":1,"b":3,"c":1,"d":4,"x":3,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":3,\"c\":1,\"d\":4,\"operation\":\"compare_at_input\",\"x\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0017","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-1)t+(4)；g:R→R，g(t)=(-1)t+(3)。在 x=4 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 3, 5；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304317,"parameters":{"operation":"compare_at_input","a":-1,"b":4,"c":-1,"d":3,"x":4,"semantic_template":"qf-composition-order-comparison/{\"a\":-1,\"b\":4,\"c\":-1,\"d\":3,\"operation\":\"compare_at_input\",\"x\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0018","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(0)t+(5)；g:R→R，g(t)=(0)t+(2)。在 x=5 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 2, 5；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304318,"parameters":{"operation":"compare_at_input","a":0,"b":5,"c":0,"d":2,"x":5,"semantic_template":"qf-composition-order-comparison/{\"a\":0,\"b\":5,\"c\":0,\"d\":2,\"operation\":\"compare_at_input\",\"x\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0019","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(6)；g:R→R，g(t)=(1)t+(1)。在 x=6 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"是","explanation_zh":"兩種順序的值分別為 13, 13；所以答案為是。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304319,"parameters":{"operation":"compare_at_input","a":1,"b":6,"c":1,"d":1,"x":6,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":6,\"c\":1,\"d\":1,\"operation\":\"compare_at_input\",\"x\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0020","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(2)t+(7)；g:R→R，g(t)=(2)t+(0)。在 x=7 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 42, 35；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304320,"parameters":{"operation":"compare_at_input","a":2,"b":7,"c":2,"d":0,"x":7,"semantic_template":"qf-composition-order-comparison/{\"a\":2,\"b\":7,\"c\":2,\"d\":0,\"operation\":\"compare_at_input\",\"x\":7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0021","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(1)t+(8)；g:R→R，g(t)=(1)t+(-1)。在 x=8 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"是","explanation_zh":"兩種順序的值分別為 15, 15；所以答案為是。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304321,"parameters":{"operation":"compare_at_input","a":1,"b":8,"c":1,"d":-1,"x":8,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":8,\"c\":1,\"d\":-1,\"operation\":\"compare_at_input\",\"x\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0022","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-3)t+(9)；g:R→R，g(t)=(-1)t+(-2)。在 x=9 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 16, 42；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304322,"parameters":{"operation":"compare_at_input","a":-3,"b":9,"c":-1,"d":-2,"x":9,"semantic_template":"qf-composition-order-comparison/{\"a\":-3,\"b\":9,\"c\":-1,\"d\":-2,\"operation\":\"compare_at_input\",\"x\":9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0023","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-2)t+(10)；g:R→R，g(t)=(0)t+(-3)。在 x=10 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -3, 16；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304323,"parameters":{"operation":"compare_at_input","a":-2,"b":10,"c":0,"d":-3,"x":10,"semantic_template":"qf-composition-order-comparison/{\"a\":-2,\"b\":10,\"c\":0,\"d\":-3,\"operation\":\"compare_at_input\",\"x\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0024","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(-1)t+(11)；g:R→R，g(t)=(1)t+(-4)。在 x=11 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 -4, 4；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304324,"parameters":{"operation":"compare_at_input","a":-1,"b":11,"c":1,"d":-4,"x":11,"semantic_template":"qf-composition-order-comparison/{\"a\":-1,\"b\":11,\"c\":1,\"d\":-4,\"operation\":\"compare_at_input\",\"x\":11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r04-composition-order-comparison-0025","batch_id":"batch-20260930-r04-composition-foundations","language":"zh-Hant","source_mko_ids":["mko-composition"],"title_zh":"兩種合成順序比較","stem_zh":"明示總函數 f:R→R，f(t)=(0)t+(12)；g:R→R，g(t)=(2)t+(-5)。在 x=12 時，(g∘f)(x) 與 (f∘g)(x) 是否相等？只比較此明示輸入。","answer":{"kind":"short_text","value":"否","explanation_zh":"兩種順序的值分別為 19, 12；所以答案為否。此題不是由單一點證明任意函數交換。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["求值順序","逐輸入比較"]},"variant":{"family_id":"qf-composition-order-comparison","seed":202609304325,"parameters":{"operation":"compare_at_input","a":0,"b":12,"c":2,"d":-5,"x":12,"semantic_template":"qf-composition-order-comparison/{\"a\":0,\"b\":12,\"c\":2,\"d\":-5,\"operation\":\"compare_at_input\",\"x\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}