IMO 2011 Shortlist A6

Let f be a function from the set of real numbers to itself that satisfies f(x + y) ≤ yf(x) + f(f(x)) for all real number...

imomathematicsolympiadshortlistalgebra

IMO 2011 Shortlist A6

Category: Algebra

Problem

Let f be a function from the set of real numbers to itself that satisfies f(x + y) ≤ yf(x) + f(f(x)) for all real numbers x and y. Prove that f(x) = 0 for all x ≤ 0.