Question 3117: Composition Value from Finite Function Tables

Original question and givens

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).

• G001 — 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).

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={-18, 0, 19}

both tables are total on their declared domains

x=4;f(x)=0;D={-18, 0, 19}

f(x)∈D=Yes

x=5;f(x)=19;D={-18, 0, 19}

f(x)∈D=Yes

x=6;f(x)=-18;D={-18, 0, 19}

f(x)∈D=Yes

x=5∈A;f(5)=19∈D

g(19)=36∈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

36

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.