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, 2004

Algebra Difficulty 2.0 Junior Prove it Canada

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

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.