Find the $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying $f(x-f(y))=1-x-y$.
We perform the substitution $(x, y) \leftarrow(x+f(0), 0)$, to find $f(x)=1-x-f(0)$. By evaluating at 0, we then find $f(0)=1-f(0)=\frac{1}{2}$. Conversely, we have $\frac{1}{2}-\left(x-\left(\frac{1}{2}-y\right)\right)=$ $1-x-y:$ the function $f: x \mapsto \frac{1}{2}-x$ is the unique solution.