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Zekrom

IMO 2011 NO 3

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Misalkan $f : \mathbb{R} \rightarrow \mathbb{R}$ adalah suatu fungsi bernilai real terdefinisi pada himpunan bagian real memenuhi 

 

$f(x+y) \leq y f(x) +f(f(x))$

 

untuk semua bilangan real $x$ dan $y$. Buktikan bahwa $f(x)=0$ untuk semua $x \leq 0$. 

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