IMO Shortlist 1983 problem 12


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2. travnja 2012.
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Find all functions f defined on the set of positive reals which take positive real values and satisfy: f(xf(y))=yf(x) for all x,y; and f(x)\to0 as x\to\infty.
Izvor: Međunarodna matematička olimpijada, shortlist 1983