Give an example of a bounded set $H \subset \mathbb{R}^p$ and a continuous function $f:H\to\mathbb{R}^q$ such that $f^{−1}$ is not continuous.

In my analysis book there is the following problem:

Give an example of a bounded set $H \subset \mathbb{R}^p$ and a continuous,injective function$f : H \to \mathbb{R}^q$ such that $f^{−1}$ is not continuous on $ f(H)$.

I tried to solve this question but I didn't reach anything useful.