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Functional equation

Source: Middle European Mathematical Olympiad 2013 T-1

May 17, 2014

functionalgebra solvedalgebraFunction equations

Problem Statement

Find all functions

f : \mathbb{R} \rightarrow \mathbb{R}

such that

f( xf(x) + 2y) = f(x^2)+f(y)+x+y-1

holds for all

x, y \in \mathbb{R}