MathDB
37th Austrian Mathematical Olympiad 2006

Source: round 3, day2, problem 2

February 10, 2009
functionalgebrafunctional equationalgebra unsolved

Problem Statement

Find all monotonous functions f:R→R f: \mathbb{R} \to \mathbb{R} that satisfy the following functional equation: f(f(x)) \equal{} f( \minus{} f(x)) \equal{} f(x)^2.