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IF x^3 + f(y)*x + f(z) = 0 THEN f(x)^3 + y*f(x) + z = 0

Source: German TST 3, P3, 2009, Exam set by Gunther Vogel

July 18, 2009

functionalgebrapolynomialcalculusGermany

Problem Statement

Find all functions

f: \mathbb{R} \mapsto \mathbb{R}

such that

\forall x,y,z \in \mathbb{R}

we have: If x^3 \plus{} f(y) \cdot x \plus{} f(z) \equal{} 0, then f(x)^3 \plus{} y \cdot f(x) \plus{} z \equal{} 0.