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YAFTFP - Yet Another "Find The Functions" Problem

Source: 38th Brazilian Undergrad MO (2016) - First Day, Problem 2

November 25, 2016
functional equation

Problem Statement

Find all functions f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} such that
f(x2+y2f(x))=xf(y)2−f(x)2 f(x^2+y^2f(x)) = xf(y)^2-f(x)^2
for every x,y∈Rx, y \in \mathbb{R}
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