Question 3120: Composition Value from Finite Function Tables

Original question and givens

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).

• G001 — 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).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-composition

Step-by-step derivation

(g∘f)(x)

g(f(x)):apply f first,then g

f:A→B;g:D→C;D={-21, 0, 22}

both tables are total on their declared domains

x=7;f(x)=0;D={-21, 0, 22}

f(x)∈D=Yes

x=8;f(x)=22;D={-21, 0, 22}

f(x)∈D=Yes

x=9;f(x)=-21;D={-21, 0, 22}

f(x)∈D=Yes

x=8∈A;f(8)=22∈D

g(22)=42∈C

Reverse checks

• S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

42

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.