Question about sets and inverse functions

Question

I was wondering if I could get some help for the following question.

Let $f: A \to B$ be a function and let $G, H$ is included in $B$. I want to prove the following statement:

If $G$ is included in $H$ then $f^{-1}(G)$ is included in $f^{-1}(H)$

I am really not sure how to prove it so any help would be appreciated!

Thanks

Answer 1

If $x\in f^{-1}(G)$, then $f(x)\in G$. Since $G\subset H$, $f(x)\in H$. Therefore, $x\in f^{-1}(H)$.