# Continuous functions

#### yo79

Find all continuous functions $$\displaystyle f: (1, \infty) \to (1, \infty)$$ such that $$\displaystyle f(\sqrt{x^2y^2-x^2-y^2+2})=\sqrt{(f(x)f(y))^2-(f(x))^2-(f(y))^2+2}, \; \forall x,y \in (1, \infty)$$.

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