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f:R->R s.t. f(f(x))-x^2+x+3=0

Source: 2004 Korea Junior Math Olympiad

June 28, 2024
functionfunctional equationExistencealgebra

Problem Statement

Show that there exists no function f:R→Rf:\mathbb {R}\rightarrow \mathbb {R} that satisfies f(f(x))−x2+x+3=0f(f(x))-x^2+x+3=0 for arbitrary real variable xx.
(Same as KMO 2004 P1)
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