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OlympiadBench / 2313 / If f(x)=x²−x+2,g(x)=ax+b, and f(g(x))=9x²−3x+2, determine all…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

answer type

Tuple

is multiple answer

true

language

English

question

f(x)=x^{2}-x+2, g(x)=a x+b

, and

f(g(x))=9 x^{2}-3 x+2

, determine all possible ordered pairs

(a, b)

which satisfy this relationship.

Plain-text mathematical notation (without MathML)

If f(x)=x²−x+2,g(x)=ax+b, and f(g(x))=9x²−3x+2, determine all possible ordered pairs (a,b) which satisfy this relationship.

Original LaTeX notation

If $f(x)=x^{2}-x+2, g(x)=a x+b$, and $f(g(x))=9 x^{2}-3 x+2$, determine all possible ordered pairs $(a, b)$ which satisfy this relationship.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2313
task_id: 6f0e673d-bb9c-565f-9225-c9ce0c82b4b9
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2313
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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