# Freaky Functions

Algebra Level 5

Suppose $f(x)$ and $g(x)$ are non-zero polynomials with real coefficients, such that $f(g(x))=f(x)\cdot g(x).$ If $g(2)=37,$ what is $g(3)?$

Details and assumptions

The zero polynomial is a polynomial that is identically 0, i.e. $f=0$.

A non-zero polynomial is a polynomial that is not the zero polynomial. Equivalently, there is a value $\alpha$ such that $f(\alpha) \neq 0$.
A non-zero polynomial is allowed to have specific values that evaluate to 0. E.g. $f(x) = x-1$ is a non-zero polynomial even though $f(1) = 0$.

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