jasperE3 07.04.2021 17:38 Find all functions $f:\mathbb R\to\mathbb R$ such that for all $x,y\in\mathbb R$, $$f(x-f(y))=1-x-y.$$
jasperE3 07.04.2021 17:39 Solution Let $P(x,y)$ be the assertion $f(x-f(y))=1-x-y$. $P(f(x),x)\Rightarrow 1-f(0)-x=f(x)$ Testing, we see that the only solution is $\boxed{f(x)=\frac12-x}$.