Calculus - function strictly increasing question

Question

Let $f : D \to\operatorname{Im}(f)$ be strictly increasing (for some $D \subseteq \mathbb{R}$). Prove that the inverse function $f^{-1}$ is strictly increasing.

How do I prove this from the definition of a strictly increasing function?

Answer 1

Hint: Let $a,b\in \operatorname{Im}(f)$ with $a