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Question 1125: Exact Affine-Function Evaluation

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0001-01125 · q-20261003-r05-linear-function-0025

Original question and givens

Over R, f(x)=(12)x+(0). Compute f(2) exactly.

  • G001 — Over R, f(x)=(12)x+(0). Compute f(2) 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.

Step-by-step derivation

S001 · implies

Before

f:R→R; f(x)=mx+b

After

m=0 gives a constant affine function

Conditions: none

An affine function allows m=0; do not impose the nondegenerate-equation condition on every affine function.

Step identifiers and dependencies

Rule: affine_domain · Uses: G001

S002 · calculation

Before

m·x := mul(12, 2)

After

m·x = 24

Conditions: none

Substitute the same input and multiply first.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S001

S003 · calculation

Before

f(x) := sum(24, 0)

After

f(x) = 24

Conditions: none

Then add the constant intercept.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S002

S004 · implies

Before

x=2; m=12; b=0

After

f(2)=24

Conditions: none

The calculation follows the original expression, retaining parentheses for negative coefficients.

Step identifiers and dependencies

Rule: substitution_identity · Uses: G001, S003

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

24

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: c058c932629330be760f69be4e582a94f9dc0eff5a7dfa60659530fbc4a1d2d7
  • candidate record SHA-256: 51f7ee8acb6b4868c65e9cd6648d95c50c84c154ffbc728b912ad2d0e0ed45d8
  • semantic review receipt SHA-256: c3b44ce8ed60ada6902fb206627537d5f90ba2a867eaba43a36f903280c496cc
  • question-first witness SHA-256: 3e91602adc7f81a2671a2a3ffaf6a447028b56abc5853e8271673d76f30cd7ad
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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