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f(2xy) + f(f(x + y)) = xf(y) + yf(x) + f(x + y)

Source: 21st Philippine Mathematical Olympiad 2019 p1

January 7, 2020
functional equationalgebra

Problem Statement

Find all functions f:Rā†’Rf : R \to R such that f(2xy)+f(f(x+y))=xf(y)+yf(x)+f(x+y)f(2xy) + f(f(x + y)) = xf(y) + yf(x) + f(x + y) for all real numbers xx and yy.
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