Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x, y \in \mathbb{R}$,

$$
f(x-f(y))=1-x-y
$$
Let $f$ be a potential solution.

By taking $x=f(y)$ in the initial equation, we obtain $f(y)=1-f(0)-y$. Thus, $f$ is of the form $x \mapsto c-x$ with $c=1-f(0)$. By substituting back into the initial equation, we deduce that for all real $x, y, c-(x-(c-y))=1-x-y$. Consequently, $c=\frac{1}{2}$, and we verify that $x \mapsto \frac{1}{2}-x$ is indeed a solution.