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f (x) + 2f (\sqrt[3]{1-x^3}) = x^3

Source: 2018 Swedish Mathematical Competition p2

May 1, 2021
algebrafunctional equationfunctional

Problem Statement

Find all functions f:R→Rf: R \to R that satisfy f(x)+2f(1−x33)=x3f (x) + 2f (\sqrt[3]{1-x^3}) = x^3 for all real xx.
(Here x3\sqrt[3]{x} is defined all over RR.)
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