I think the answer depends on what exactly you mean by $f^{-1}$.
One has the usual inverse image sheaf $f^{-1} \mathcal F$.
However, in the case of $\mathcal O$-modules (where $(X,\mathcal O)$ is a scheme), one usually considers a variant of $f^{-1}$. Namely:
Let $f : X \to Y$ be any morphism of schemes and let $\mathcal F$ be a $\mathcal O_Y$-module on $Y$.
Then one defines the pullback $f^{*}\mathcal F := f^{-1}\mathcal F \otimes_{f^{-1}\mathcal O_Y} \mathcal O_X$, which is a $\mathcal O_X$-module on $X$.
Using this notion of pullback, one can show that quasi-coherent sheaves on $Y$ pull back to quasi-coherent sheaves on $X$ and also for example that rank $n$ vector bundles pull back to rank $n$ vector bundles.