Let
be any function that maps the set of real numbers into the set of real numbers. Prove that there exist real numbers
and
such that
Proposed by Igor Voronovich, Belarus
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Let $f$ be any function that maps the set of real numbers into the set of real numbers. Prove that there exist real numbers $x$ and $y$ such that $$f\left(x-f(y)\right)>yf(x)+x$$
Proposed by Igor Voronovich, Belarus