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Functional equation, IMO 1997 Shortlist

Source: IMO Shortlist 1997, Q22

August 31, 2003
functionalgebrafunctional equationpolynomialIMO Shortlist

Problem Statement

Does there exist functions f,g:Rā†’R 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 x a) if k \equal{} 3? b) if k \equal{} 4?
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