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

Source: Kosovo TST 2020 Problem 1

February 8, 2020
functional equationfunctionalgebra

Problem Statement

Find all functions f:Rā†’Rf:\mathbb{R}\rightarrow\mathbb{R} such that, for all real numbers xx and yy satisfy, f(x+yf(x+y))=y2+f(x)f(y)f\left(x+yf(x+y)\right)=y^2+f(x)f(y)
Proposed by Dorlir Ahmeti, Kosovo
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