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f(g(x)) = x^3 and g(f(x)) = x^2.

Source: 2022 Saudi Arabia March Camp Test p2 BMO + EGMO TST

May 13, 2024
algebra

Problem Statement

Determine if there exist functions f,g:R→Rf, g : R \to R satisfying for every x∈Rx \in R the following equations f(g(x))=x3f(g(x)) = x^3 and g(f(x))=x2g(f(x)) = x^2.
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