IMO 2009 Shortlist A5

Let f be any function that maps the set of real numbers into the set of real numbers. Prove that there exist real number...

imomathematicsolympiadshortlistalgebra

IMO 2009 Shortlist A5

Category: Algebra

Problem

Let f be any function that maps the set of real numbers into the set of real numbers. Prove that there exist real numbers x and y such that f (x − f(y)) > yf(x) + x.