{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0001","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae853705c2f4b6954d907a6fbb7c65e1a20652c421f2dd875897f15d7a95b5a7","family_id":"qf-composition-affine-evaluation","seed":202609304001,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-3,\"b\":-12,\"c\":-2,\"d\":6,\"operation\":\"g_after_f\",\"x\":-12}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-3)t+(-12) and g:R→R be g(t)=(-2)t+(6). Find (g∘f)(-12) exactly.","answer":{"kind":"short_text","value":"-42","explanation":"First f(-12)=24; then g(f(-12))=-42."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0002","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c5e3efe81619aa75a4281f59230122f703cbd455c1b5e05e2e5c84002c8ad9a7","family_id":"qf-composition-affine-evaluation","seed":202609304002,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-2,\"b\":-11,\"c\":-1,\"d\":5,\"operation\":\"g_after_f\",\"x\":-11}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-2)t+(-11) and g:R→R be g(t)=(-1)t+(5). Find (g∘f)(-11) exactly.","answer":{"kind":"short_text","value":"-6","explanation":"First f(-11)=11; then g(f(-11))=-6."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0003","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8917c93a5789812b15a5fba875b5078e524c44aa481dbdb1fd9713d6d0d9b457","family_id":"qf-composition-affine-evaluation","seed":202609304003,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-1,\"b\":-10,\"c\":0,\"d\":4,\"operation\":\"g_after_f\",\"x\":-10}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-1)t+(-10) and g:R→R be g(t)=(0)t+(4). Find (g∘f)(-10) exactly.","answer":{"kind":"short_text","value":"4","explanation":"First f(-10)=0; then g(f(-10))=4."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0004","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01cc73ccf42a431bc609abd1801e273cac7fc304bad1309e7c866ffefd197fde","family_id":"qf-composition-affine-evaluation","seed":202609304004,"semantic_template":"qf-composition-affine-evaluation/{\"a\":0,\"b\":-9,\"c\":1,\"d\":3,\"operation\":\"g_after_f\",\"x\":-9}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(0)t+(-9) and g:R→R be g(t)=(1)t+(3). Find (g∘f)(-9) exactly.","answer":{"kind":"short_text","value":"-6","explanation":"First f(-9)=-9; then g(f(-9))=-6."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0005","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"595e1f80e0cb3c3d1bef9f5640884fe5d7228fe5bea9c2042b449c839664429d","family_id":"qf-composition-affine-evaluation","seed":202609304005,"semantic_template":"qf-composition-affine-evaluation/{\"a\":1,\"b\":-8,\"c\":2,\"d\":2,\"operation\":\"g_after_f\",\"x\":-8}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(1)t+(-8) and g:R→R be g(t)=(2)t+(2). Find (g∘f)(-8) exactly.","answer":{"kind":"short_text","value":"-30","explanation":"First f(-8)=-16; then g(f(-8))=-30."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0006","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"107aa73172ed8eef4a2999cea1d7c8c8e507a32d9416750a3448893239238afa","family_id":"qf-composition-affine-evaluation","seed":202609304006,"semantic_template":"qf-composition-affine-evaluation/{\"a\":2,\"b\":-7,\"c\":-2,\"d\":1,\"operation\":\"g_after_f\",\"x\":-7}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(2)t+(-7) and g:R→R be g(t)=(-2)t+(1). Find (g∘f)(-7) exactly.","answer":{"kind":"short_text","value":"43","explanation":"First f(-7)=-21; then g(f(-7))=43."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0007","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ebe8903b6219f1da1fa025968d37be236167a6692134f434fa6b3a7519cd8b0","family_id":"qf-composition-affine-evaluation","seed":202609304007,"semantic_template":"qf-composition-affine-evaluation/{\"a\":3,\"b\":-6,\"c\":-1,\"d\":0,\"operation\":\"g_after_f\",\"x\":-6}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(3)t+(-6) and g:R→R be g(t)=(-1)t+(0). Find (g∘f)(-6) exactly.","answer":{"kind":"short_text","value":"24","explanation":"First f(-6)=-24; then g(f(-6))=24."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0008","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"72e86002e0a066ef0823c14c6faa977a5a5b53e79dac25c78750b375032301f0","family_id":"qf-composition-affine-evaluation","seed":202609304008,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-3,\"b\":-5,\"c\":0,\"d\":-1,\"operation\":\"g_after_f\",\"x\":-5}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-3)t+(-5) and g:R→R be g(t)=(0)t+(-1). Find (g∘f)(-5) exactly.","answer":{"kind":"short_text","value":"-1","explanation":"First f(-5)=10; then g(f(-5))=-1."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0009","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8137c45d8a76f333a4df8f6ae35eb297c3dee004fe35d0e1bd507428a31808f7","family_id":"qf-composition-affine-evaluation","seed":202609304009,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-2,\"b\":-4,\"c\":1,\"d\":-2,\"operation\":\"g_after_f\",\"x\":-4}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-2)t+(-4) and g:R→R be g(t)=(1)t+(-2). Find (g∘f)(-4) exactly.","answer":{"kind":"short_text","value":"2","explanation":"First f(-4)=4; then g(f(-4))=2."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0010","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4843aa27aaf463eee163b10caf04aa8f64443ed4ca93ce2b4a1e80446736fd8","family_id":"qf-composition-affine-evaluation","seed":202609304010,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-1,\"b\":-3,\"c\":2,\"d\":-3,\"operation\":\"g_after_f\",\"x\":-3}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-1)t+(-3) and g:R→R be g(t)=(2)t+(-3). Find (g∘f)(-3) exactly.","answer":{"kind":"short_text","value":"-3","explanation":"First f(-3)=0; then g(f(-3))=-3."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0011","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5f7bf1463d7238a60c1665e311707ed7c0db87afd4c18f47f91f489739d13d71","family_id":"qf-composition-affine-evaluation","seed":202609304011,"semantic_template":"qf-composition-affine-evaluation/{\"a\":0,\"b\":-2,\"c\":-2,\"d\":-4,\"operation\":\"g_after_f\",\"x\":-2}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(0)t+(-2) and g:R→R be g(t)=(-2)t+(-4). Find (g∘f)(-2) exactly.","answer":{"kind":"short_text","value":"0","explanation":"First f(-2)=-2; then g(f(-2))=0."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0012","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c7e54fdd29f69843ba9776d5ebd276f383517401002b90e3fed2941a2f32e87","family_id":"qf-composition-affine-evaluation","seed":202609304012,"semantic_template":"qf-composition-affine-evaluation/{\"a\":1,\"b\":-1,\"c\":-1,\"d\":-5,\"operation\":\"g_after_f\",\"x\":-1}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(1)t+(-1) and g:R→R be g(t)=(-1)t+(-5). Find (g∘f)(-1) exactly.","answer":{"kind":"short_text","value":"-3","explanation":"First f(-1)=-2; then g(f(-1))=-3."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0013","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e567d5c1e3b24fc79f3b5a9fb011e8c35c6f60a1981ecc6a013425ce305bbc06","family_id":"qf-composition-affine-evaluation","seed":202609304013,"semantic_template":"qf-composition-affine-evaluation/{\"a\":2,\"b\":0,\"c\":0,\"d\":-6,\"operation\":\"g_after_f\",\"x\":0}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(2)t+(0) and g:R→R be g(t)=(0)t+(-6). Find (g∘f)(0) exactly.","answer":{"kind":"short_text","value":"-6","explanation":"First f(0)=0; then g(f(0))=-6."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0014","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48507226757910a22e4777499282936c49c09d9359ce94400cf540e909a571ac","family_id":"qf-composition-affine-evaluation","seed":202609304014,"semantic_template":"qf-composition-affine-evaluation/{\"a\":3,\"b\":1,\"c\":1,\"d\":6,\"operation\":\"g_after_f\",\"x\":1}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(3)t+(1) and g:R→R be g(t)=(1)t+(6). Find (g∘f)(1) exactly.","answer":{"kind":"short_text","value":"10","explanation":"First f(1)=4; then g(f(1))=10."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0015","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e3da04ca560964c365d45d6b122ce85181aa085d0e68ec55e6468f545db47543","family_id":"qf-composition-affine-evaluation","seed":202609304015,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-3,\"b\":2,\"c\":2,\"d\":5,\"operation\":\"g_after_f\",\"x\":2}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-3)t+(2) and g:R→R be g(t)=(2)t+(5). Find (g∘f)(2) exactly.","answer":{"kind":"short_text","value":"-3","explanation":"First f(2)=-4; then g(f(2))=-3."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0016","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"409e1efa86ee14eea2fa289d6a43a53546b3a4aefc873551a103dbd4c748bbe9","family_id":"qf-composition-affine-evaluation","seed":202609304016,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-2,\"b\":3,\"c\":-2,\"d\":4,\"operation\":\"g_after_f\",\"x\":3}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-2)t+(3) and g:R→R be g(t)=(-2)t+(4). Find (g∘f)(3) exactly.","answer":{"kind":"short_text","value":"10","explanation":"First f(3)=-3; then g(f(3))=10."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0017","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7424be0d384bb86e7e022a632cc9af56c3903d43eefef411668325a2784d0598","family_id":"qf-composition-affine-evaluation","seed":202609304017,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-1,\"b\":4,\"c\":-1,\"d\":3,\"operation\":\"g_after_f\",\"x\":4}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-1)t+(4) and g:R→R be g(t)=(-1)t+(3). Find (g∘f)(4) exactly.","answer":{"kind":"short_text","value":"3","explanation":"First f(4)=0; then g(f(4))=3."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0018","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb402fde11458846f7774ad618188707a50d16c6b1a8e84c09aeb03e0552018c","family_id":"qf-composition-affine-evaluation","seed":202609304018,"semantic_template":"qf-composition-affine-evaluation/{\"a\":0,\"b\":5,\"c\":0,\"d\":2,\"operation\":\"g_after_f\",\"x\":5}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(0)t+(5) and g:R→R be g(t)=(0)t+(2). Find (g∘f)(5) exactly.","answer":{"kind":"short_text","value":"2","explanation":"First f(5)=5; then g(f(5))=2."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0019","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e887dbea38dc7c04bd7233857e5058902ef9e1be03becf7db617c301721fbdcc","family_id":"qf-composition-affine-evaluation","seed":202609304019,"semantic_template":"qf-composition-affine-evaluation/{\"a\":1,\"b\":6,\"c\":1,\"d\":1,\"operation\":\"g_after_f\",\"x\":6}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(1)t+(6) and g:R→R be g(t)=(1)t+(1). Find (g∘f)(6) exactly.","answer":{"kind":"short_text","value":"13","explanation":"First f(6)=12; then g(f(6))=13."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0020","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00cbd9ac499fcb3a22f0afed5a37aa4ca80cffc488c65d9f69abdc1378c4c5ac","family_id":"qf-composition-affine-evaluation","seed":202609304020,"semantic_template":"qf-composition-affine-evaluation/{\"a\":2,\"b\":7,\"c\":2,\"d\":0,\"operation\":\"g_after_f\",\"x\":7}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(2)t+(7) and g:R→R be g(t)=(2)t+(0). Find (g∘f)(7) exactly.","answer":{"kind":"short_text","value":"42","explanation":"First f(7)=21; then g(f(7))=42."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0021","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29b0272e3f009ad716532b7115cbeff369095f2a4c46a195aaf4b295f0d95c1e","family_id":"qf-composition-affine-evaluation","seed":202609304021,"semantic_template":"qf-composition-affine-evaluation/{\"a\":3,\"b\":8,\"c\":-2,\"d\":-1,\"operation\":\"g_after_f\",\"x\":8}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(3)t+(8) and g:R→R be g(t)=(-2)t+(-1). Find (g∘f)(8) exactly.","answer":{"kind":"short_text","value":"-65","explanation":"First f(8)=32; then g(f(8))=-65."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0022","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e3e860af27ba076a21dd11b7d8c2a8d5f28062d4d93ee564c92304b4f432277","family_id":"qf-composition-affine-evaluation","seed":202609304022,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-3,\"b\":9,\"c\":-1,\"d\":-2,\"operation\":\"g_after_f\",\"x\":9}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-3)t+(9) and g:R→R be g(t)=(-1)t+(-2). Find (g∘f)(9) exactly.","answer":{"kind":"short_text","value":"16","explanation":"First f(9)=-18; then g(f(9))=16."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0023","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3f3091747e8ad9690368cead58d73860dc115d68dd1734f5fe1ded0578972a20","family_id":"qf-composition-affine-evaluation","seed":202609304023,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-2,\"b\":10,\"c\":0,\"d\":-3,\"operation\":\"g_after_f\",\"x\":10}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-2)t+(10) and g:R→R be g(t)=(0)t+(-3). Find (g∘f)(10) exactly.","answer":{"kind":"short_text","value":"-3","explanation":"First f(10)=-10; then g(f(10))=-3."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0024","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d0c6586caf7288f0281cbbe42ff347237f54858ff7313beaf18730de804c1028","family_id":"qf-composition-affine-evaluation","seed":202609304024,"semantic_template":"qf-composition-affine-evaluation/{\"a\":-1,\"b\":11,\"c\":1,\"d\":-4,\"operation\":\"g_after_f\",\"x\":11}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(-1)t+(11) and g:R→R be g(t)=(1)t+(-4). Find (g∘f)(11) exactly.","answer":{"kind":"short_text","value":"-4","explanation":"First f(11)=0; then g(f(11))=-4."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-affine-evaluation-0025","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"085e0e2bc0c4daf234f653b8083487499dcd5aa9fff5fa6a19e245c194a8ce8d","family_id":"qf-composition-affine-evaluation","seed":202609304025,"semantic_template":"qf-composition-affine-evaluation/{\"a\":0,\"b\":12,\"c\":2,\"d\":-5,\"operation\":\"g_after_f\",\"x\":12}"},"fields":{"title":"Composition of Explicit Affine Expressions","stem":"Let f:R→R be f(t)=(0)t+(12) and g:R→R be g(t)=(2)t+(-5). Find (g∘f)(12) exactly.","answer":{"kind":"short_text","value":"19","explanation":"First f(12)=12; then g(f(12))=19."},"skills":["inner function before outer function","exact substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0001","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f742854e48533d26735074607827010de9494b98f1b523deb2b76649213eb214","family_id":"qf-composition-table-evaluation","seed":202609304101,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-12, -11, -10}, B={-2, 0, 3}, C={-1, 0, 4}, f=[(-12, -2), (-11, 0), (-10, 3)], and g=[(-2, -1), (0, 4), (3, 0)]. Find (g∘f)(-12).","answer":{"kind":"short_text","value":"-1","explanation":"First read f(-12)=-2, then use that intermediate input in g to obtain -1."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0002","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bbf7cf35fd7134f8c685068f3fddc3eb46ca4e29680e5aa99f8a251d3219257f","family_id":"qf-composition-table-evaluation","seed":202609304102,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-11, -10, -9}, B={-3, 0, 4}, C={-3, 0, 6}, f=[(-11, 0), (-10, 4), (-9, -3)], and g=[(-3, 0), (0, -3), (4, 6)]. Find (g∘f)(-10).","answer":{"kind":"short_text","value":"6","explanation":"First read f(-10)=4, then use that intermediate input in g to obtain 6."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0003","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f3ce4342996d3f48abd1d3f2cd31d45f9102540039b702dac231bc38174aed21","family_id":"qf-composition-table-evaluation","seed":202609304103,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-10, -9, -8}, B={-4, 0, 5}, C={-5, 0, 8}, f=[(-10, 5), (-9, -4), (-8, 0)], and g=[(-4, 8), (0, 0), (5, -5)]. Find (g∘f)(-8).","answer":{"kind":"short_text","value":"0","explanation":"First read f(-8)=0, then use that intermediate input in g to obtain 0."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0004","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"02bb4169ef63ef9372132fa28e8a6a78151634a452f7570e179cee75ede551b7","family_id":"qf-composition-table-evaluation","seed":202609304104,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-9, -8, -7}, B={-5, 0, 6}, C={-7, 0, 10}, f=[(-9, -5), (-8, 0), (-7, 6)], and g=[(-5, -7), (0, 10), (6, 0)]. Find (g∘f)(-9).","answer":{"kind":"short_text","value":"-7","explanation":"First read f(-9)=-5, then use that intermediate input in g to obtain -7."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0005","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a206ba0a1a296c37a57c507de3dc9e65238aac9963634c8f5d2d833354e6ab14","family_id":"qf-composition-table-evaluation","seed":202609304105,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-8, -7, -6}, B={-6, 0, 7}, C={-9, 0, 12}, f=[(-8, 0), (-7, 7), (-6, -6)], and g=[(-6, 0), (0, -9), (7, 12)]. Find (g∘f)(-7).","answer":{"kind":"short_text","value":"12","explanation":"First read f(-7)=7, then use that intermediate input in g to obtain 12."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0006","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3612affb3d55bf69aea12bdba05ededc19fc9a74d1f2218a95dffc47bdc88ba5","family_id":"qf-composition-table-evaluation","seed":202609304106,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-7, -6, -5}, B={-7, 0, 8}, C={-11, 0, 14}, f=[(-7, 8), (-6, -7), (-5, 0)], and g=[(-7, 14), (0, 0), (8, -11)]. Find (g∘f)(-5).","answer":{"kind":"short_text","value":"0","explanation":"First read f(-5)=0, then use that intermediate input in g to obtain 0."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0007","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ffbb914b39e2543ed71221196d16bac77238ecbcd8f82acf4ca7fdad69a6a876","family_id":"qf-composition-table-evaluation","seed":202609304107,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-6, -5, -4}, B={-8, 0, 9}, C={-13, 0, 16}, f=[(-6, -8), (-5, 0), (-4, 9)], and g=[(-8, -13), (0, 16), (9, 0)]. Find (g∘f)(-6).","answer":{"kind":"short_text","value":"-13","explanation":"First read f(-6)=-8, then use that intermediate input in g to obtain -13."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0008","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e3dd2e5c25e1c19c53f9af9bb52b99d1ff507d2fe08a5ca6c0c8dbd14ee06b46","family_id":"qf-composition-table-evaluation","seed":202609304108,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-5, -4, -3}, B={-9, 0, 10}, C={-15, 0, 18}, f=[(-5, 0), (-4, 10), (-3, -9)], and g=[(-9, 0), (0, -15), (10, 18)]. Find (g∘f)(-4).","answer":{"kind":"short_text","value":"18","explanation":"First read f(-4)=10, then use that intermediate input in g to obtain 18."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0009","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"69e51a4a76f7c20cf89453b6cbc8d1098bacedcd5ed0409781d5856b0dada6ae","family_id":"qf-composition-table-evaluation","seed":202609304109,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-4, -3, -2}, B={-10, 0, 11}, C={-17, 0, 20}, f=[(-4, 11), (-3, -10), (-2, 0)], and g=[(-10, 20), (0, 0), (11, -17)]. Find (g∘f)(-2).","answer":{"kind":"short_text","value":"0","explanation":"First read f(-2)=0, then use that intermediate input in g to obtain 0."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0010","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cff1196ffa15dedf46264bcc73176a02ee743fafb9a66fde94382dcf4735db10","family_id":"qf-composition-table-evaluation","seed":202609304110,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-3, -2, -1}, B={-11, 0, 12}, C={-19, 0, 22}, f=[(-3, -11), (-2, 0), (-1, 12)], and g=[(-11, -19), (0, 22), (12, 0)]. Find (g∘f)(-3).","answer":{"kind":"short_text","value":"-19","explanation":"First read f(-3)=-11, then use that intermediate input in g to obtain -19."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0011","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6413d570de2983ec8c80c867b829e202c89c27c346f672fed2878c5e8d0db7c","family_id":"qf-composition-table-evaluation","seed":202609304111,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-2, -1, 0}, B={-12, 0, 13}, C={-21, 0, 24}, f=[(-2, 0), (-1, 13), (0, -12)], and g=[(-12, 0), (0, -21), (13, 24)]. Find (g∘f)(-1).","answer":{"kind":"short_text","value":"24","explanation":"First read f(-1)=13, then use that intermediate input in g to obtain 24."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0012","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a03577b0c54cc7cf21689d2dbf55241afa3ab2ad2c22ae56b917cf817d602ddb","family_id":"qf-composition-table-evaluation","seed":202609304112,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={-1, 0, 1}, B={-13, 0, 14}, C={-23, 0, 26}, f=[(-1, 14), (0, -13), (1, 0)], and g=[(-13, 26), (0, 0), (14, -23)]. Find (g∘f)(1).","answer":{"kind":"short_text","value":"0","explanation":"First read f(1)=0, then use that intermediate input in g to obtain 0."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0013","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae1598710270116e16a7557b8c1179412aedb68862103f798b7d7258a9669886","family_id":"qf-composition-table-evaluation","seed":202609304113,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={0, 1, 2}, B={-14, 0, 15}, C={-25, 0, 28}, f=[(0, -14), (1, 0), (2, 15)], and g=[(-14, -25), (0, 28), (15, 0)]. Find (g∘f)(0).","answer":{"kind":"short_text","value":"-25","explanation":"First read f(0)=-14, then use that intermediate input in g to obtain -25."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0014","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65ce60e75de4ee608aa7c7dd4bcb8d41421ffe15a14215d1abe614afc8e8dabb","family_id":"qf-composition-table-evaluation","seed":202609304114,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={1, 2, 3}, B={-15, 0, 16}, C={-27, 0, 30}, f=[(1, 0), (2, 16), (3, -15)], and g=[(-15, 0), (0, -27), (16, 30)]. Find (g∘f)(2).","answer":{"kind":"short_text","value":"30","explanation":"First read f(2)=16, then use that intermediate input in g to obtain 30."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0015","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4007c9da4cdd17fd93a1504d1aee5e7a0df0fcbb613dc421c2488467882b1977","family_id":"qf-composition-table-evaluation","seed":202609304115,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={2, 3, 4}, B={-16, 0, 17}, C={-29, 0, 32}, f=[(2, 17), (3, -16), (4, 0)], and g=[(-16, 32), (0, 0), (17, -29)]. Find (g∘f)(4).","answer":{"kind":"short_text","value":"0","explanation":"First read f(4)=0, then use that intermediate input in g to obtain 0."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0016","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e50c4447bd79a2e3af6194fc81cb966185d35e7d261d5f2e613a6852dd1f0a44","family_id":"qf-composition-table-evaluation","seed":202609304116,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={3, 4, 5}, B={-17, 0, 18}, C={-31, 0, 34}, f=[(3, -17), (4, 0), (5, 18)], and g=[(-17, -31), (0, 34), (18, 0)]. Find (g∘f)(3).","answer":{"kind":"short_text","value":"-31","explanation":"First read f(3)=-17, then use that intermediate input in g to obtain -31."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0017","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"13b9396dc5207277793e2ee5be382f14364f0bc9904c9c6c0487f4f775d9faa1","family_id":"qf-composition-table-evaluation","seed":202609304117,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={4, 5, 6}, B={-18, 0, 19}, C={-33, 0, 36}, f=[(4, 0), (5, 19), (6, -18)], and g=[(-18, 0), (0, -33), (19, 36)]. Find (g∘f)(5).","answer":{"kind":"short_text","value":"36","explanation":"First read f(5)=19, then use that intermediate input in g to obtain 36."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0018","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e8d559c15ae807d2a5d309866b3b686227a9c316b6903143c8ea38627ba14a5c","family_id":"qf-composition-table-evaluation","seed":202609304118,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={5, 6, 7}, B={-19, 0, 20}, C={-35, 0, 38}, f=[(5, 20), (6, -19), (7, 0)], and g=[(-19, 38), (0, 0), (20, -35)]. Find (g∘f)(7).","answer":{"kind":"short_text","value":"0","explanation":"First read f(7)=0, then use that intermediate input in g to obtain 0."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0019","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f47c66716eb8d53a7aaa2007b4ad993b7863145bc86c2bcb368cd8c94c09ea71","family_id":"qf-composition-table-evaluation","seed":202609304119,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={6, 7, 8}, B={-20, 0, 21}, C={-37, 0, 40}, f=[(6, -20), (7, 0), (8, 21)], and g=[(-20, -37), (0, 40), (21, 0)]. Find (g∘f)(6).","answer":{"kind":"short_text","value":"-37","explanation":"First read f(6)=-20, then use that intermediate input in g to obtain -37."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0020","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40f66660bd07c2eaea1011b33582164aca498230fde90b82c12ceffdb06aab0c","family_id":"qf-composition-table-evaluation","seed":202609304120,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={7, 8, 9}, B={-21, 0, 22}, C={-39, 0, 42}, f=[(7, 0), (8, 22), (9, -21)], and g=[(-21, 0), (0, -39), (22, 42)]. Find (g∘f)(8).","answer":{"kind":"short_text","value":"42","explanation":"First read f(8)=22, then use that intermediate input in g to obtain 42."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0021","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09e7e80db625c7c1fe8f416153590a9c8e8f9ffb99735e8a553d984bada5bb46","family_id":"qf-composition-table-evaluation","seed":202609304121,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={8, 9, 10}, B={-22, 0, 23}, C={-41, 0, 44}, f=[(8, 23), (9, -22), (10, 0)], and g=[(-22, 44), (0, 0), (23, -41)]. Find (g∘f)(10).","answer":{"kind":"short_text","value":"0","explanation":"First read f(10)=0, then use that intermediate input in g to obtain 0."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0022","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db7e2fa1bce0785ab27b05642f73e94cd0e409656f1a4caa66e04970dcf4a823","family_id":"qf-composition-table-evaluation","seed":202609304122,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={9, 10, 11}, B={-23, 0, 24}, C={-43, 0, 46}, f=[(9, -23), (10, 0), (11, 24)], and g=[(-23, -43), (0, 46), (24, 0)]. Find (g∘f)(9).","answer":{"kind":"short_text","value":"-43","explanation":"First read f(9)=-23, then use that intermediate input in g to obtain -43."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0023","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31945f1625cb13f6f43f3e518f635d20cb5784c2d6c5dad02b78bf549006db7a","family_id":"qf-composition-table-evaluation","seed":202609304123,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={10, 11, 12}, B={-24, 0, 25}, C={-45, 0, 48}, f=[(10, 0), (11, 25), (12, -24)], and g=[(-24, 0), (0, -45), (25, 48)]. Find (g∘f)(11).","answer":{"kind":"short_text","value":"48","explanation":"First read f(11)=25, then use that intermediate input in g to obtain 48."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0024","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23d17ec566c1f1ac92a319ccf28d7740c16bfe4c7b96391a6acd85cadf466fa5","family_id":"qf-composition-table-evaluation","seed":202609304124,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={11, 12, 13}, B={-25, 0, 26}, C={-47, 0, 50}, f=[(11, 26), (12, -25), (13, 0)], and g=[(-25, 50), (0, 0), (26, -47)]. Find (g∘f)(13).","answer":{"kind":"short_text","value":"0","explanation":"First read f(13)=0, then use that intermediate input in g to obtain 0."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-table-evaluation-0025","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c68f6399257a412b98bed0da104c299065ed4821aa8bcde8d39dc90e716cbd6c","family_id":"qf-composition-table-evaluation","seed":202609304125,"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}"},"fields":{"title":"Composition Value from Finite Function Tables","stem":"The explicit total functions have A={12, 13, 14}, B={-26, 0, 27}, C={-49, 0, 52}, f=[(12, -26), (13, 0), (14, 27)], and g=[(-26, -49), (0, 52), (27, 0)]. Find (g∘f)(12).","answer":{"kind":"short_text","value":"-49","explanation":"First read f(12)=-26, then use that intermediate input in g to obtain -49."},"skills":["intermediate value","composition of total functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0001","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"95febdb7badd401f38b64e8d22bfc905eb069c5657ec9d9890db597849e99e7a","family_id":"qf-composition-domain-set","seed":202609304201,"semantic_template":"qf-composition-domain-set/{\"A\":[],\"B\":[0],\"C\":[],\"D\":[],\"F\":[],\"G\":[],\"operation\":\"restricted_domain\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A=∅, B={0}, D=∅, C=∅, f=[], and g=[]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"∅","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is ∅; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0002","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"572d32aaace55cae1338d511b7ec9f810ad9e2c95ee90379760284086874417e","family_id":"qf-composition-domain-set","seed":202609304202,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-1, 0, 1}, B={-2, 0, 2}, D=∅, C={5}, f=[(-1, -2), (0, 0), (1, 2)], and g=[]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"∅","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is ∅; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0003","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a6ec8abc52259a8d12564c50d4736a9e8576cbc373593cdfebc823e286e72d8c","family_id":"qf-composition-domain-set","seed":202609304203,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-10, -9, -8}, B={-4, 0, 5}, D={-4, 0}, C={-4, 1, 5}, f=[(-10, 5), (-9, -4), (-8, 0)], and g=[(-4, 5), (0, -4)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{-9, -8}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {-9, -8}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0004","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e8292c580c816b51369e40ed19015dd38cb684cdf0e573d91041cb8a1104d4d2","family_id":"qf-composition-domain-set","seed":202609304204,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-9, -8, -7}, B={-5, 0, 6}, D={102}, C={-6, 1, 7}, f=[(-9, -5), (-8, 0), (-7, 6)], and g=[(102, -6)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"∅","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is ∅; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0005","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"24935ef923cdc8a173574b57c9b762a16ed348dfec9cbbfd25a95ccadac009c2","family_id":"qf-composition-domain-set","seed":202609304205,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-8, -7, -6}, B={-6, 0, 7}, D={-6, 0, 7}, C={-8, 1, 9}, f=[(-8, 0), (-7, 7), (-6, -6)], and g=[(-6, 1), (0, 9), (7, -8)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{-8, -7, -6}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {-8, -7, -6}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0006","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef23a19b0abe7f5cb0145987a684310fb4408586cc6bb2b70ca54776712c4b99","family_id":"qf-composition-domain-set","seed":202609304206,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-7, -6, -5}, B={-7, 0, 8}, D={0}, C={-10, 1, 11}, f=[(-7, 8), (-6, -7), (-5, 0)], and g=[(0, 11)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{-5}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {-5}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0007","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f682818e7690e816c6a99c68a76c92a773e7d0cb426fb9e87fc4b8da5593dc48","family_id":"qf-composition-domain-set","seed":202609304207,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-6, -5, -4}, B={-8, 0, 9}, D={-8, 0}, C={-12, 1, 13}, f=[(-6, -8), (-5, 0), (-4, 9)], and g=[(-8, -12), (0, 1)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{-6, -5}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {-6, -5}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0008","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c95334ff82806aad29d5bad9de71931755cf2fa05ec8e06f6bfc7ba7b0a07fe3","family_id":"qf-composition-domain-set","seed":202609304208,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-5, -4, -3}, B={-9, 0, 10}, D={106}, C={-14, 1, 15}, f=[(-5, 0), (-4, 10), (-3, -9)], and g=[(106, 1)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"∅","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is ∅; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0009","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"734b4a88402e4d2044f5e483efbcc7cc0410bfe441b4f9eeb709c98e33e710d7","family_id":"qf-composition-domain-set","seed":202609304209,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-4, -3, -2}, B={-10, 0, 11}, D={-10, 0, 11}, C={-16, 1, 17}, f=[(-4, 11), (-3, -10), (-2, 0)], and g=[(-10, 17), (0, -16), (11, 1)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{-4, -3, -2}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {-4, -3, -2}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0010","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a2cc6f892ba167d646133d1efd16674654ff01cabd5e53cc9a885268137278d","family_id":"qf-composition-domain-set","seed":202609304210,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-3, -2, -1}, B={-11, 0, 12}, D={0}, C={-18, 1, 19}, f=[(-3, -11), (-2, 0), (-1, 12)], and g=[(0, -18)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{-2}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {-2}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0011","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a866fb16674728d0fc08eac1755b38a457476c0d11a1578ff2e0f548e54969f","family_id":"qf-composition-domain-set","seed":202609304211,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-2, -1, 0}, B={-12, 0, 13}, D={-12, 0}, C={-20, 1, 21}, f=[(-2, 0), (-1, 13), (0, -12)], and g=[(-12, 1), (0, 21)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{-2, 0}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {-2, 0}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0012","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f617b13e25f68d853b512b6ff7c3cec93aa63714fde80c6b47d65cbf681a4de","family_id":"qf-composition-domain-set","seed":202609304212,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={-1, 0, 1}, B={-13, 0, 14}, D={110}, C={-22, 1, 23}, f=[(-1, 14), (0, -13), (1, 0)], and g=[(110, 23)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"∅","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is ∅; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0013","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a3bc6e511d2b619800ea370105563e883ff365461acca4b030eace48705b9b5","family_id":"qf-composition-domain-set","seed":202609304213,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={0, 1, 2}, B={-14, 0, 15}, D={-14, 0, 15}, C={-24, 1, 25}, f=[(0, -14), (1, 0), (2, 15)], and g=[(-14, -24), (0, 1), (15, 25)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{0, 1, 2}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {0, 1, 2}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0014","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e52c21dff3b7bceb74f9b8e32e5d2acb3daaa6880d648c45de67406103aaafe","family_id":"qf-composition-domain-set","seed":202609304214,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={1, 2, 3}, B={-15, 0, 16}, D={0}, C={-26, 1, 27}, f=[(1, 0), (2, 16), (3, -15)], and g=[(0, 1)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{1}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {1}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0015","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d5252d024c6d1931647bc2f3e8347c9ff6035d95b9752777bafd43ee17af765","family_id":"qf-composition-domain-set","seed":202609304215,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={2, 3, 4}, B={-16, 0, 17}, D={-16, 0}, C={-28, 1, 29}, f=[(2, 17), (3, -16), (4, 0)], and g=[(-16, 29), (0, -28)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{3, 4}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {3, 4}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0016","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"46b5eac63aa50eb333905771a6914749353f5754f6fb5e324b77783c8247808b","family_id":"qf-composition-domain-set","seed":202609304216,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={3, 4, 5}, B={-17, 0, 18}, D={114}, C={-30, 1, 31}, f=[(3, -17), (4, 0), (5, 18)], and g=[(114, -30)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"∅","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is ∅; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0017","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66c377a0a94433d2479fe33c6bb3f2741159792540d16fb33ffd87fdd8967be5","family_id":"qf-composition-domain-set","seed":202609304217,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={4, 5, 6}, B={-18, 0, 19}, D={-18, 0, 19}, C={-32, 1, 33}, f=[(4, 0), (5, 19), (6, -18)], and g=[(-18, 1), (0, 33), (19, -32)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{4, 5, 6}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {4, 5, 6}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0018","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"badb54fa50d86c05e9fe09ce2358e83473df502941318aaed89a4547483b742b","family_id":"qf-composition-domain-set","seed":202609304218,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={5, 6, 7}, B={-19, 0, 20}, D={0}, C={-34, 1, 35}, f=[(5, 20), (6, -19), (7, 0)], and g=[(0, 35)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{7}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {7}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0019","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3898627bd6e66731ac6c9fac6fd08807f296d2e7e11700b0f672d2c1baab84d2","family_id":"qf-composition-domain-set","seed":202609304219,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={6, 7, 8}, B={-20, 0, 21}, D={-20, 0}, C={-36, 1, 37}, f=[(6, -20), (7, 0), (8, 21)], and g=[(-20, -36), (0, 1)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{6, 7}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {6, 7}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0020","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"526e6e72919759f9594fc45fe5a3a4f7aa907d4d6eb49b5da35e97550cb4128d","family_id":"qf-composition-domain-set","seed":202609304220,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={7, 8, 9}, B={-21, 0, 22}, D={118}, C={-38, 1, 39}, f=[(7, 0), (8, 22), (9, -21)], and g=[(118, 1)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"∅","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is ∅; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0021","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7df78aa1148240a8b92f38d0df58ec6a25fd20bbeaeb8918fdad51713bb7f16a","family_id":"qf-composition-domain-set","seed":202609304221,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={8, 9, 10}, B={-22, 0, 23}, D={-22, 0, 23}, C={-40, 1, 41}, f=[(8, 23), (9, -22), (10, 0)], and g=[(-22, 41), (0, -40), (23, 1)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{8, 9, 10}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {8, 9, 10}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0022","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a232da979ffd1490285c2431a383fe04d681febb0ab4a4f0f013c313faf18d8b","family_id":"qf-composition-domain-set","seed":202609304222,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={9, 10, 11}, B={-23, 0, 24}, D={0}, C={-42, 1, 43}, f=[(9, -23), (10, 0), (11, 24)], and g=[(0, -42)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{10}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {10}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0023","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c147c428563b1bc0f7fe25c7768ddcb1626f3156df1d6572956a68372572654c","family_id":"qf-composition-domain-set","seed":202609304223,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={10, 11, 12}, B={-24, 0, 25}, D={-24, 0}, C={-44, 1, 45}, f=[(10, 0), (11, 25), (12, -24)], and g=[(-24, 1), (0, 45)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{10, 12}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {10, 12}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0024","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"375465ac45446fcd1827f08aee8129419adf764136e6f5a32b0c61f21af3cc04","family_id":"qf-composition-domain-set","seed":202609304224,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={11, 12, 13}, B={-25, 0, 26}, D={122}, C={-46, 1, 47}, f=[(11, 26), (12, -25), (13, 0)], and g=[(122, 47)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"∅","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is ∅; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-domain-set-0025","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4dfc8f0b25ad303c934fdbeeeb019e7aca82aa334d7e46ca0cbf4a06797b8e5","family_id":"qf-composition-domain-set","seed":202609304225,"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\"}"},"fields":{"title":"Permitted Domain of a Restricted Composition","stem":"Let f:A→B and g:D→C be the explicit total functions A={12, 13, 14}, B={-26, 0, 27}, D={-26, 0, 27}, C={-48, 1, 49}, f=[(12, -26), (13, 0), (14, 27)], and g=[(-26, -48), (0, 1), (27, 49)]. List {x∈A:f(x)∈D}.","answer":{"kind":"short_text","value":"{12, 13, 14}","explanation":"Check each input in A and retain it exactly when its f-value lies in D. The permitted composition domain is {12, 13, 14}; it may be empty."},"skills":["intermediate-value compatibility","empty-set boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0001","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc8b6ac7e2c154f4c84f3cdc46604990432b71cd2024507ad461f66696d3d0fd","family_id":"qf-composition-order-comparison","seed":202609304301,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-12,\"c\":1,\"d\":6,\"operation\":\"compare_at_input\",\"x\":-12}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(1)t+(-12) and g(t)=(1)t+(6). At the explicit input x=-12, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"The two values are -18 and -18, so the answer is Yes. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0002","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1103c1294cd2632d7296edd557c17f56ffedee90f3133f49c59b91e905a45745","family_id":"qf-composition-order-comparison","seed":202609304302,"semantic_template":"qf-composition-order-comparison/{\"a\":-2,\"b\":-11,\"c\":-1,\"d\":5,\"operation\":\"compare_at_input\",\"x\":-11}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-2)t+(-11) and g(t)=(-1)t+(5). At the explicit input x=-11, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -6 and -43, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0003","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a6560a6ea8b2dce6d6d00d68da246c9b5943b603095f1e44fefeefde9369898","family_id":"qf-composition-order-comparison","seed":202609304303,"semantic_template":"qf-composition-order-comparison/{\"a\":-1,\"b\":-10,\"c\":0,\"d\":4,\"operation\":\"compare_at_input\",\"x\":-10}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-1)t+(-10) and g(t)=(0)t+(4). At the explicit input x=-10, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 4 and -14, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0004","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60a4cd08895c97df7b2c6131fcad1c409558b365de9fa20c188913606800d097","family_id":"qf-composition-order-comparison","seed":202609304304,"semantic_template":"qf-composition-order-comparison/{\"a\":0,\"b\":-9,\"c\":1,\"d\":3,\"operation\":\"compare_at_input\",\"x\":-9}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(0)t+(-9) and g(t)=(1)t+(3). At the explicit input x=-9, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -6 and -9, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0005","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7575110400ea773159d92ae8afbf7b050d51f262fcb0d6a32f5a45e3008a0827","family_id":"qf-composition-order-comparison","seed":202609304305,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-8,\"c\":2,\"d\":2,\"operation\":\"compare_at_input\",\"x\":-8}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(1)t+(-8) and g(t)=(2)t+(2). At the explicit input x=-8, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -30 and -22, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0006","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"30d0be43fc5057c45e7ce8859241751eeb7a0ed3629b796db3555433186cb5fd","family_id":"qf-composition-order-comparison","seed":202609304306,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-7,\"c\":1,\"d\":1,\"operation\":\"compare_at_input\",\"x\":-7}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(1)t+(-7) and g(t)=(1)t+(1). At the explicit input x=-7, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"The two values are -13 and -13, so the answer is Yes. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0007","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a89a52d368fa5c88b375be9fa5904cd11464330d1b503847f2a6492a8c86359b","family_id":"qf-composition-order-comparison","seed":202609304307,"semantic_template":"qf-composition-order-comparison/{\"a\":3,\"b\":-6,\"c\":-1,\"d\":0,\"operation\":\"compare_at_input\",\"x\":-6}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(3)t+(-6) and g(t)=(-1)t+(0). At the explicit input x=-6, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 24 and 12, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0008","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4e7dd7208f4b18ef68ecc6cd80ad88fb4d2b45df7f5963ec565a959aafb8715","family_id":"qf-composition-order-comparison","seed":202609304308,"semantic_template":"qf-composition-order-comparison/{\"a\":-3,\"b\":-5,\"c\":0,\"d\":-1,\"operation\":\"compare_at_input\",\"x\":-5}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-3)t+(-5) and g(t)=(0)t+(-1). At the explicit input x=-5, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -1 and -2, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0009","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"afa8442ffa3922898c743a8ddb7fd6b64d1c8a11d39420f230797934f5c56376","family_id":"qf-composition-order-comparison","seed":202609304309,"semantic_template":"qf-composition-order-comparison/{\"a\":-2,\"b\":-4,\"c\":1,\"d\":-2,\"operation\":\"compare_at_input\",\"x\":-4}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-2)t+(-4) and g(t)=(1)t+(-2). At the explicit input x=-4, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 2 and 8, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0010","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45168c6155e0e590f3995bea0e91e376d95490758abab2b3ad58c56a4d1ac805","family_id":"qf-composition-order-comparison","seed":202609304310,"semantic_template":"qf-composition-order-comparison/{\"a\":-1,\"b\":-3,\"c\":2,\"d\":-3,\"operation\":\"compare_at_input\",\"x\":-3}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-1)t+(-3) and g(t)=(2)t+(-3). At the explicit input x=-3, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -3 and 6, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0011","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"439f9b684ce5cf1422dc9361073433c859392be8499b80eb7ae727e94b8cc724","family_id":"qf-composition-order-comparison","seed":202609304311,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-2,\"c\":1,\"d\":-4,\"operation\":\"compare_at_input\",\"x\":-2}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(1)t+(-2) and g(t)=(1)t+(-4). At the explicit input x=-2, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"The two values are -8 and -8, so the answer is Yes. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0012","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e89cc695505a97aac2ce756be3f60f5a1bda9f2f57d9c981861af6f7da8b28e4","family_id":"qf-composition-order-comparison","seed":202609304312,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":-1,\"c\":-1,\"d\":-5,\"operation\":\"compare_at_input\",\"x\":-1}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(1)t+(-1) and g(t)=(-1)t+(-5). At the explicit input x=-1, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -3 and -5, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0013","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"99bd4a42138d9d44561117b807ab69edeb1084ef88f6365b5efa4e682ea22d40","family_id":"qf-composition-order-comparison","seed":202609304313,"semantic_template":"qf-composition-order-comparison/{\"a\":2,\"b\":0,\"c\":0,\"d\":-6,\"operation\":\"compare_at_input\",\"x\":0}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(2)t+(0) and g(t)=(0)t+(-6). At the explicit input x=0, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -6 and -12, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0014","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a4027cc49b912b7d2fa572404882cfda701ccd175486ccabe60090f4c01274b9","family_id":"qf-composition-order-comparison","seed":202609304314,"semantic_template":"qf-composition-order-comparison/{\"a\":3,\"b\":1,\"c\":1,\"d\":6,\"operation\":\"compare_at_input\",\"x\":1}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(3)t+(1) and g(t)=(1)t+(6). At the explicit input x=1, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 10 and 22, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0015","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"105f0b0d20548494e05d518ea313b9663d5240cf6a9e44961b9e86c494a181ae","family_id":"qf-composition-order-comparison","seed":202609304315,"semantic_template":"qf-composition-order-comparison/{\"a\":-3,\"b\":2,\"c\":2,\"d\":5,\"operation\":\"compare_at_input\",\"x\":2}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-3)t+(2) and g(t)=(2)t+(5). At the explicit input x=2, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -3 and -25, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0016","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"190c022539dd64ca2d7688d89c49b13b96fb95c95bb179c9846aecaec66548ac","family_id":"qf-composition-order-comparison","seed":202609304316,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":3,\"c\":1,\"d\":4,\"operation\":\"compare_at_input\",\"x\":3}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(1)t+(3) and g(t)=(1)t+(4). At the explicit input x=3, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"The two values are 10 and 10, so the answer is Yes. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0017","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d13365be22efd828c479290554035a3df70fe12d08d96f2e831c31f313a44e2e","family_id":"qf-composition-order-comparison","seed":202609304317,"semantic_template":"qf-composition-order-comparison/{\"a\":-1,\"b\":4,\"c\":-1,\"d\":3,\"operation\":\"compare_at_input\",\"x\":4}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-1)t+(4) and g(t)=(-1)t+(3). At the explicit input x=4, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 3 and 5, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0018","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5c4f5a691270c3d86c54b2085c63f9fd36bb49e5ba58ec51898c33f91d3de4e","family_id":"qf-composition-order-comparison","seed":202609304318,"semantic_template":"qf-composition-order-comparison/{\"a\":0,\"b\":5,\"c\":0,\"d\":2,\"operation\":\"compare_at_input\",\"x\":5}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(0)t+(5) and g(t)=(0)t+(2). At the explicit input x=5, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 2 and 5, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0019","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6d74f616e748aeb8a90e7ae30cb9d833d3807be682491abde9ad7dcb8b4be6b4","family_id":"qf-composition-order-comparison","seed":202609304319,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":6,\"c\":1,\"d\":1,\"operation\":\"compare_at_input\",\"x\":6}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(1)t+(6) and g(t)=(1)t+(1). At the explicit input x=6, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"The two values are 13 and 13, so the answer is Yes. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0020","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bba58e6304b4f2c5ddd6a3c7cd604d3163e89503bf9aab2836472e84d3e1d88e","family_id":"qf-composition-order-comparison","seed":202609304320,"semantic_template":"qf-composition-order-comparison/{\"a\":2,\"b\":7,\"c\":2,\"d\":0,\"operation\":\"compare_at_input\",\"x\":7}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(2)t+(7) and g(t)=(2)t+(0). At the explicit input x=7, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 42 and 35, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0021","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d62ddab20800f59a44804d489258faa9bf0b2e7b0af9e90329d8624675946e4e","family_id":"qf-composition-order-comparison","seed":202609304321,"semantic_template":"qf-composition-order-comparison/{\"a\":1,\"b\":8,\"c\":1,\"d\":-1,\"operation\":\"compare_at_input\",\"x\":8}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(1)t+(8) and g(t)=(1)t+(-1). At the explicit input x=8, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"Yes","explanation":"The two values are 15 and 15, so the answer is Yes. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0022","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2aaf669376c4b3442930cf3e96b59938f14db3363c89f20884806558fa23d47a","family_id":"qf-composition-order-comparison","seed":202609304322,"semantic_template":"qf-composition-order-comparison/{\"a\":-3,\"b\":9,\"c\":-1,\"d\":-2,\"operation\":\"compare_at_input\",\"x\":9}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-3)t+(9) and g(t)=(-1)t+(-2). At the explicit input x=9, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 16 and 42, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0023","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"11dad6d91ab5f09d0e6230b02a93633ca8363616cb56a5f23bbd162c119f112a","family_id":"qf-composition-order-comparison","seed":202609304323,"semantic_template":"qf-composition-order-comparison/{\"a\":-2,\"b\":10,\"c\":0,\"d\":-3,\"operation\":\"compare_at_input\",\"x\":10}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-2)t+(10) and g(t)=(0)t+(-3). At the explicit input x=10, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -3 and 16, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0024","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6108646a782a36274063a250fb9b2fac52cbce8eebda1a88939d8d60a09d70ba","family_id":"qf-composition-order-comparison","seed":202609304324,"semantic_template":"qf-composition-order-comparison/{\"a\":-1,\"b\":11,\"c\":1,\"d\":-4,\"operation\":\"compare_at_input\",\"x\":11}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(-1)t+(11) and g(t)=(1)t+(-4). At the explicit input x=11, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are -4 and 4, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r04-composition-order-comparison-0025","batch_id":"batch-20260930-r04-composition-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dee699da48fb07e535fcb34f24db01581d48cabd2c6cab44adac05d4806c473a","family_id":"qf-composition-order-comparison","seed":202609304325,"semantic_template":"qf-composition-order-comparison/{\"a\":0,\"b\":12,\"c\":2,\"d\":-5,\"operation\":\"compare_at_input\",\"x\":12}"},"fields":{"title":"Comparing Two Composition Orders","stem":"Let f(t)=(0)t+(12) and g(t)=(2)t+(-5). At the explicit input x=12, are (g∘f)(x) and (f∘g)(x) equal?","answer":{"kind":"short_text","value":"No","explanation":"The two values are 19 and 12, so the answer is No. Equality or inequality at this one input does not prove a general commutativity claim."},"skills":["evaluation order","input-by-input comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}