# 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.

• Why not post what problems your having or what you've tried? It really helps to know what an OP is struggling with exactly. Sometimes you might be misunderstanding something or not fully understanding something and answerers on here can bridge the gap or provide valuable insight. Like a guy said in a movie once "You gotta milk it" :) Otherwise, you could just find the proof on Google.. – user70962 Jun 9 '13 at 8:14
• Oh... I missed that point. thanks for your advice! I will soon! – syko Jun 9 '13 at 8:30

For $f : \mathbb{R}^n \to \mathbb{R}^n$, consider $F : \mathbb{R}^n\times\mathbb{R}^n \to \mathbb{R}^n$ given by $F({\bf x}, {\bf y}) = f({\bf y}) - {\bf x}$.
• I thought you should have written $F(x,y)=y-f(x)$ – user344374 Dec 27 '17 at 15:21