CIIM 2016 Problem 1

Find all functions $f:(0,+\infty) \to (0,+\infty)$ that satisfy $(i)$ $f(xf(y))=yf(x), \forall x,y > 0,$ $(ii)$ $\lim_{x\to+\infty} f(x) = 0.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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