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A Functional Equation

Source: 2011 Philippine Math Olympiad National Stage Problem 4

July 15, 2013
functionalgebra unsolvedalgebra

Problem Statement

Find all (if there is one) functions f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} such that for all x∈Rx\in\mathbb{R}, f(f(x))+xf(x)=1.f(f(x))+xf(x)=1.
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