olymmath

ISL 2009 A5

    Let ff be any function that maps the set of real numbers into the set of real numbers. Prove that there exist real numbers xx and yy such that f(x−f(y))>yf(x)+xf(x-f(y))>y f(x)+x

    Dataset text NuminaMath olympiads. Quoted with source.

    Official text: IMO 2009 Shortlist booklet, page 6.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

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