IMO 2018 Shortlist A5

Determine all fun tions f : p0,8q Ñ R satisfying ˆ x x ˙ fpyq “ fpxyq f ´y x ¯ for all x,y ą 0. (South Korea)

IMO 2018 Shortlist A5

Category: Algebra

Problem

Determine all fun tions f : p0,8q Ñ R satisfying ˆ x x ˙ fpyq “ fpxyq f ´y x ¯ for all x,y ą 0. (South Korea)