Continuous functions

Jan 2013
96
0
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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