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easy functional equation

Source: 2023 4th OMpD L3 P1 - Brazil - Olimpíada Matemáticos por Diversão

September 21, 2023
functionfunctional equationreal numberalgebra

Problem Statement

Determine all functions f:Rā†’Rf : \mathbb{R} \rightarrow \mathbb{R} such that, for all real numbers xx and yy, f(x)(x+f(f(y)))=f(x2)+xf(y)f(x)(x+f(f(y))) = f(x^2)+xf(y)
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