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BALTIC-WAY 2015 Problem 5

  • Answer

Find all functions f:R→Rf: \mathbf{R} \rightarrow \mathbf{R} satisfying the equation

∣x∣f(y)+yf(x)=f(xy)+f(x2)+f(f(y))|x| f(y)+y f(x)=f(x y)+f\left(x^{2}\right)+f(f(y))

for all real numbers xx and yy.

Dataset text NuminaMath olympiads. Quoted with source.

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f(x)=c(|x|-x), \text{ where } c \geq 0

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