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What is the value of $ g (x + f (y) $?

Source: Brazilian Math Olympiad - University Level - Galois-Noether 2018 #2

November 24, 2019
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Problem Statement

Let f,g:R→R f, g: \mathbb {R} \to \mathbb {R} function such that f(x+g(y))=−x+y+1 f (x + g (y)) = - x + y + 1 for each pair of real numbers x x e y y . What is the value of g(x+f(y) g (x + f (y) ?
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