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 ˘...
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)