4b

Part of 2023 Abelkonkurransen Finale

Problems(1)

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

Source: 2023 Abelkonkurransen Finale, Problem 4b

Find all functions

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

\mathbb R^{+}

is the set of all positive real numbers.

functional equationalgebra