Question 1120: Exact Affine-Function Evaluation

Original question and givens

Over R, f(x)=(7)x+(2). Compute f(-3) exactly.

• G001 — Over R, f(x)=(7)x+(2). Compute f(-3) exactly.

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-linear-function

Step-by-step derivation

f:R→R; f(x)=mx+b

m=0 gives a constant affine function

m·x := mul(7, -3)

m·x = -21

f(x) := sum(-21, 2)

f(x) = -19

x=-3; m=7; b=2

f(-3)=-19

Reverse checks

• 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 — Recompute f(x) with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute m·x with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

-19

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.