real analysis - If$f^{-1}(x)=kx-f(x)$, then what can we say about $f$?

If $f^{-1}(x)=kx-f(x)\forall x\in\mathbb{R}$ for a strictly increasing $f$ and $k$ a constant, then what can be said about $f$?

I think the answer is of the form $f(x)=x+c$, for some $c\in\mathbb{R}$. Any hints. Thanks beforehand