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Polynomial functional equation!

Source: Iran TST 2012-Second exam-1st day-P2

May 12, 2012
algebrapolynomialfunctionalgebra proposed

Problem Statement

Let g(x)g(x) be a polynomial of degree at least 22 with all of its coefficients positive. Find all functions f:R+⟶R+f:\mathbb R^+ \longrightarrow \mathbb R^+ such that f(f(x)+g(x)+2y)=f(x)+g(x)+2f(y)   \forall x,y\in \mathbb R^+.
Proposed by Mohammad Jafari
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