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Iran function (third round)

Source: Iran MO 3rd round midterm exam

July 28, 2019
functional equationIran

Problem Statement

Find all function f:Rā†’Rf:\mathbb{R}\rightarrow \mathbb{R} such that for any three real number a,b,ca,b,c , if a+f(b)+f(f(c))=0 a + f(b) + f(f(c)) = 0 : f(a)3+bf(b)2+c2f(c)=3abc f(a)^3 + bf(b)^2 + c^2f(c) = 3abc .
Proposed by Amirhossein Zolfaghari
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