IMO Shortlist 1994 problem A3


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2. travnja 2012.
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Let S be the set of all real numbers strictly greater than −1. Find all functions f: S \to S satisfying the two conditions:

(a) f(x + f(y) + xf(y)) = y + f(x) + yf(x) for all x, y in S;

(b) \frac {f(x)}{x} is strictly increasing on each of the two intervals - 1 < x < 0 and 0 < x.
Izvor: Međunarodna matematička olimpijada, shortlist 1994