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Found problems: 1

VI Soros Olympiad 1999 - 2000 (Russia), 9.4
Is there a function $f(x)$, which satisfies both of the following conditions: a) if $x \ne y$, then $f(x)\ne f(y)$ b) for all real $x$, holds the inequality $f(x^2-1998x)-f^2(2x-1999)\ge \frac14$?
functional inequation inequalities functional algebra functional equations