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BALKAN-SL 2021 A5

  • Answer

Find all functions f:R+⟶R+f: \mathbb{R}^{+} \longrightarrow \mathbb{R}^{+}such that

f(xf(x+y))=yf(x)+1f(x f(x+y))=y f(x)+1

holds for all x,y∈R+x, y \in \mathbb{R}^{+}.

Dataset text NuminaMath olympiads. Quoted with source.

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f(x)=\frac{1}{x}

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