Question 3108: Composition Value from Finite Function Tables

Original question and givens

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).

• G001 — 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).

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={-9, 0, 10}

both tables are total on their declared domains

x=-5;f(x)=0;D={-9, 0, 10}

f(x)∈D=Yes

x=-4;f(x)=10;D={-9, 0, 10}

f(x)∈D=Yes

x=-3;f(x)=-9;D={-9, 0, 10}

f(x)∈D=Yes

x=-4∈A;f(-4)=10∈D

g(10)=18∈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

18

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.