# Fractions Fun with Functions

Algebra Level 5

Let $$f(x)$$ be a polynomial with integer coefficients defined by $$f:\mathbb{R}^+\to \mathbb{R}^+$$ satisfying $\dfrac{f(x)}{x}=\sqrt{\dfrac{f(f(x))}{f(x)}}$

Find the sum of all possible values of $$f(3)$$ subject to $$f(3) < 100$$.

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