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f(f(x)-y)f(x+f(y))=x^2-y^2 , f: R \to R$

Source: Rioplatense Olympiad 2001 level 3 P4

September 6, 2018
functional equationFind all functionsalgebra

Problem Statement

Find all functions f:R→Rf: R \to R such that, for any x,y∈Rx, y \in R: f(f(x)−y)⋅f(x+f(y))=x2−y2f\left( f\left( x \right)-y \right)\cdot f\left( x+f\left( y \right) \right)={{x}^{2}}-{{y}^{2}}
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