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BALKAN 2021 Problem 2

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Find all functions f:(0,+∞)→(0,+∞)f:(0,+\infty) \rightarrow(0,+\infty) such that

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

holds for all x,y∈(0,+∞)x, y \in(0,+\infty).

Dataset text NuminaMath olympiads. Quoted with source.

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f(x)=x

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