Fractions Fun with Functions

Algebra Level 5

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

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

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