2011 IMO Problems/Problem 3
Let 
be a real-valued function defined on the set of real numbers that satisfies ![\[f(x + y) \le yf(x) + f(f(x))\]](http://latex.artofproblemsolving.com/6/3/e/63e20e9b2787ab8d177c6406d9db72cdbada44ad.png)
for all real numbers 
and 
. Prove that 
for all 
.
Solution
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