Difference between revisions of "2011 IMO Problems/Problem 3"

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==See Also==
 
==See Also==
 
*[[IMO Problems and Solutions]]
 
*[[IMO Problems and Solutions]]
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[[Category:Olympiad Algebra Problems]]
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[[Category:Functional Equation Problems]]

Revision as of 08:50, 19 July 2016

Let $f: \mathbb R \to \mathbb R$ be a real-valued function defined on the set of real numbers that satisfies \[f(x + y) \le yf(x) + f(f(x))\] for all real numbers $x$ and $y$. Prove that $f(x) = 0$ for all $x \le 0$.

Solution

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See Also