Difference between revisions of "2011 IMO Problems/Problem 3"
Humzaiqbal (talk | contribs) (Created page with "Let f : R → R be a real-valued function defined on the set of real numbers that satisfies f(x + y) ≤ yf(x) + f(f(x)) for all real numbers x and y. Prove that f(x) = 0 for all...") |
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| − | Let f : R | + | Let <math>f: \mathbb R \to \mathbb R</math> be a real-valued function defined on the set of real numbers that satisfies <cmath> f(x + y) \le yf(x) + f(f(x)) </cmath> for all real numbers <math>x</math> and <math>y</math>. Prove that <math>f(x) = 0</math> for all <math>x \le 0</math>. |
| + | |||
| + | ==Solution== | ||
| + | {{solution}} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[IMO Problems and Solutions]] | ||
| + | |||
| + | [[Category:Olympiad Algebra Problems]] | ||
| + | [[Category:Functional Equation Problems]] | ||
Revision as of 08:50, 19 July 2016
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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