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ISL 2018 A5

    Determine all functions f:(0,∞)→Rf:(0, \infty) \rightarrow \mathbb{R} satisfying (x+1x)f(y)=f(xy)+f(yx)\left(x+\frac{1}{x}\right) f(y)=f(x y)+f\left(\frac{y}{x}\right) for all x,y>0x, y>0. (South Korea)

    Dataset text NuminaMath olympiads. Quoted with source.

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