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easy functional equation f(x+a)=f(x)-x

Source: Romanian IMO TST 2005 - day 4, problem 1

April 23, 2005
functioninductionalgebra proposedalgebra

Problem Statement

Let a∈R−{0}a\in\mathbb{R}-\{0\}. Find all functions f:R→Rf: \mathbb{R}\to\mathbb{R} such that f(a+x)=f(x)−xf(a+x) = f(x) - x for all x∈Rx\in\mathbb{R}. Dan Schwartz
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