How to prove that the implicit function theorem implies the inverse function theorem?
I can prove the converse of it, but I cannot do this one. Here is the problem:
Prove that the implicit function theorem implies the inverse function theorem.
Solution 1:
For $f : \mathbb{R}^n \to \mathbb{R}^n$, consider $F : \mathbb{R}^n\times\mathbb{R}^n \to \mathbb{R}^n$ given by $F({\bf x}, {\bf y}) = f({\bf y}) - {\bf x}$.