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
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
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