A Cubic Functional Equation

★ 8/10functions Substitution algebra Functional Equations

Problem

Find all functions $f:\mathbb R\to\mathbb R$ such that for all $x,y\in\mathbb R$ ,

f(x^3)+f(y^3)=(x+y)\bigl[f(x^2)+f(y^2)-f(xy)\bigr].

Answer

Solution

Difficulty	8/10
Topics	functions, Substitution, algebra, Functional Equations

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