IMO 2022 Shortlist A3
Let Rą0 be the set of positive real numbers. Find all functions f : Rą0 Ñ Rą0 such that, for every x P Rą0, there exists...
Category: Algebra
Problem
Let Rą0 be the set of positive real numbers. Find all functions f : Rą0 Ñ Rą0 such that, for every x P Rą0, there exists a unique y P Rą0 satisfying xfpyq ` yfpxq ď 2. (Netherlands)