Determine the functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that

$$
f(x-f(y))=1-x-y
$$
We choose $x=f(y)$ then

$$
f(0)=1-f(y)-y
$$

so $f(y)=1-f(0)-y$. In particular, $f(0)=1-f(0)$, hence $f(0)=1 / 2$. We verify

$$
f(x-f(y))=f(x-1 / 2+y)=1 / 2-x+1 / 2-y=1-x-y
$$