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functional equation

Source: 2016 Korea Winter Program Test1 Day1 #3

January 25, 2016
functional equationalgebraalgebra proposed

Problem Statement

Determine all the functions f:Rā†’Rf : \mathbb{R}\rightarrow\mathbb{R} that satisfies the following.
f(xf(y)+yf(z)+zf(x))=yf(x)+zf(y)+xf(z)f(xf(y)+yf(z)+zf(x))=yf(x)+zf(y)+xf(z)
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