in a research project, I need to apply some version of the inverse function theorem to a function $f:R^m\rightarrow R^n$ with $n>m$. More specifically, I have $\gamma=f(t)$, where $\gamma$ has higher dimension. I need conditions under which $t=f^{-1}(\gamma)$ exists. However, the versions of inverse function theorems I found online (such as https://students.iiserkol.ac.in/~sp17rs038/blog/Inverse%20Function%20Theorem.pdf) have $m=n$.
If you could provide a specific reference that satisfies my need, that would be great. Thanks!