22

Part of 1997 IMO Shortlist

Problems(1)

Functional equation, IMO 1997 Shortlist

Source: IMO Shortlist 1997, Q22

Does there exist functions

f,g: \mathbb{R}\to\mathbb{R}

such that f(g(x)) \equal{} x^2 and g(f(x)) \equal{} x^k for all real numbers

x

a) if k \equal{} 3? b) if k \equal{} 4?

functionalgebrafunctional equationpolynomialIMO Shortlist