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Polish 2nd stage 2010, 5th problem (functional equation)

Source:

November 11, 2010
functionalgebra proposedalgebra

Problem Statement

Find all monotonic functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} satisfying f(f(x)−y)+f(x+y)=0,f(f(x) - y) + f(x+y) = 0, for every real x,yx, y. (Note that monotonic means that function is not increasing or not decreasing)
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