# Polynomials of polynomials

Level pending

Let $$f$$ be a (possibly constant) polynomial such that for all real $$x$$:

$$f(f(x) + f(-x)) = 9f(x^2)$$

The largest possible value of $$f(9)$$ can be expressed as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. Find $$ab$$.

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