Bounded Homeomorphism and its inverse

Question

Can someone help with an explanation on how to about this question.

Let ϕ:Rn→Rn be a homeomorphism of the form $ϕ(x)=x+h(x)$ with bounded h. Show that $ϕ^{−1}(x)=x+k(x)$, where k(x) is again bounded (with the same bound).

Answer 1

$$\phi^{-1}(x)-x= \phi^{-1}(x)-\phi( \phi^{-1}(x))=-h(\phi^{-1}(x)) $$

Define $$k(x):=-h(\phi^{-1}(x))$$