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f(xf(x) + f(y)) = y + f(x)^2

Source: Switzerland - 2004 Swiss MO Final Round p4

December 26, 2022
algebrafunctionalfunctional equation

Problem Statement

Determine all functions f:R→Rf : R \to R such that for all x,y∈Rx, y \in R holds f(xf(x)+f(y))=y+f(x)2f(xf(x) + f(y)) = y + f(x)^2
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