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1994 IMO Problems/Problem 5

Revision as of 15:49, 6 October 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>S</math> be the set of real numbers strictly greater than <math>-1</math>. Find all functions <math>f:S \to S</math> satisfying the two conditions: 1....")
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Problem

Let $S$ be the set of real numbers strictly greater than $-1$. Find all functions $f:S \to S$ satisfying the two conditions:

1. $f(x+f(y)+xf(y)) = y+f(x)+yf(x)$ for all $x$ and $y$ in $S$;

2. $\frac{f(x)}{x}$ is strictly increasing on each of the intervals $-1<x<0$ and $0<x$.

Solution

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