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

Source: 2021 Ukraine NMO 11.4

April 2, 2021
functional equationfunctionalalgebra

Problem Statement

Find all the following functions f:Rā†’Rf:R\to R , which for arbitrary valid x,yx,y holds equality: f(xf(x+y))+f((x+y)f(y))=(x+y)2f(xf(x+y))+f((x+y)f(y))=(x+y)^2 (Vadym Koval)
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