KöMaL 2021 B5197

Let $\mathbb{N}$ denote the set of non-negative integers, and let $k$ be a given positive integer. Is there a monotonically increasing function $f \colon \mathbb{N} \to \mathbb{N}$ such that $f\big(f(x)\big) = f(x) + x + k$ for all $x \in \mathbb{N}$?