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BALKAN-SL 2017 A6

  • Answer

Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} satisfying

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

for all real numbers xx and yy.

Dataset text NuminaMath olympiads. Quoted with source.

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f(x)=0 \quad \forall x \in \mathbb{R} \text{ and } f(x)=x \quad \forall x \in \mathbb{R}

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