International Mathematical Olympiad, IMO 2022, Problem 2

I present a solution to problem 2 from IMO 2022. This is an interesting math competition question that is asking us to find all functions satisfying a certain property. I discuss the details of how to approach this problem, breaking down the problem into steps until we obtain a solution. IMO Problems:    • IMO, The International Mathematical Olympiad   Putnam Problems:    • Putnam Math Competition   IMO 2023: Problem 1:    • International Math Olympiad, IMO 2023, Pro...   Problem 2:    • International Math Olympiad, IMO 2023, Pro...   Problem 4:    • International Math Olympiad, IMO 2023, Pro...   Problem 5:    • International Math Olympiad, IMO 2023, Pro...   IMO 2022: Problem 2:    • International Mathematical Olympiad, IMO 2...   IMO 2021: Problem 1:    • International Math Olympiad, IMO 2021, Pro...   A1:    • International Math Olympiad, IMO 2021, Sho...   A2:    • International Math Olympiad, IMO 2021, Sho...   A3:    • International Math Olympiad, IMO 2021, Sho...   C1:    • International Math Olympiad, IMO 2021, Sho...   IMO 2020: Problem 2:    • International Math Olympiad, IMO 2020, Pro...   IMO 2019: N2:    • International Math Olympiad, IMO 2019, Sho...   IMO 1961: Problem 1:    • International Math Olympiad, IMO 1961, Pro...