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...

IMO 2022 Shortlist A3

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)