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Functional equation f(f(x)+y) = f(y) + x on positive reals

Source: 2023 Abelkonkurransen Finale, Problem 4b

March 12, 2024
functional equationalgebra

Problem Statement

Find all functions f:R+ā†’R+f: \mathbb R^{+} \to \mathbb R^{+} satisfying \begin{align*} f(f(x)+y) = f(y) + x, \qquad \text{for all } x,y \in \mathbb R^{+}. \end{align*} Note that R+\mathbb R^{+} is the set of all positive real numbers.
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