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variation of f(g(x)+g(y))=f(g(y))-y (same thing though)

Source: Romania National Olympiad 2015, grade x, p.3

August 23, 2019
functionalgebra

Problem Statement

Find all functions f,g:Q⟶Q f,g:\mathbb{Q}\longrightarrow\mathbb{Q} that verify the relations {f(g(x)+g(y))=f(g(x))+yg(f(x)+f(y))=g(f(x))+y, \left\{\begin{matrix} f(g(x)+g(y))=f(g(x))+y \\ g(f(x)+f(y))=g(f(x))+y\end{matrix}\right. , for all x,y∈Q. x,y\in\mathbb{Q} .
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