# 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>. |

## Revision as of 13:38, 27 November 2011

Let be a real-valued function defined on the set of real numbers that satisfies for all real numbers and . Prove that for all .