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f(x + yf(x)) = f(xf(y)) - x + f(y + f(x))

Source: Switzerland - 2017 Swiss MO Final Round p2

December 30, 2022
algebrafunctionalfunctional equation

Problem Statement

Find all functions f : R→RR \to R such that for all x,y∈Rx, y \in R: f(x+yf(x))=f(xf(y))−x+f(y+f(x)).f(x + yf(x)) = f(xf(y)) - x + f(y + f(x)).
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