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Functional equation

Source: Serbian Mathematical Olympiad 2021, P5

May 14, 2021
functional equationfunctionalgebra

Problem Statement

Find all functions f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} such that for every x,y∈Rx,y\in\mathbb{R} the following equality holds: f(xf(y)+x2+y)=f(x)f(y)+xf(x)+f(y).f(xf(y)+x^2+y)=f(x)f(y)+xf(x)+f(y).
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