# Have fun with functions!

Algebra Level 4

Consider a function $$f: \mathbb R - \{ -1,0,1 \} \rightarrow \mathbb R$$ that satisfies the functional relation

$f(x)^2 \times f \left( \dfrac{1-x}{1+x} \right) = x^3 \, .$

If $$f(10)$$ is the form of $$\dfrac ab$$, where $$b$$ is positive and $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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