IMO 2023 Shortlist A4

Let Rą0 be the set of positive real numbers. Determine all functions f : Rą0 Ñ Rą0 such that x fpxq fpyq ˘ ě fpfpxqq y ˘...

IMO 2023 Shortlist A4

Category: Algebra

Problem

Let Rą0 be the set of positive real numbers. Determine all functions f : Rą0 Ñ Rą0 such that x fpxq fpyq ˘ ě fpfpxqq y ˘ fpyq for every x,y P Rą0. (Belgium)