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yoyo_fen

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**Implicit => inverse function theorem (urgent due to exam, please help)**

## Homework Statement

Prove the inverse function theorem, knowing the implicit function theorem.

## Homework Equations

The statements of both theorems... Can't think of much else.

## The Attempt at a Solution

Alright... I have a feeling that this is going to come up on my exam which is only two days from now, so please help me :(

I got a hint today: define g(x,y) = f(x)-y or g(x,y)=f(y)-x, the guy was not sure. I presume it should be the first because then the derivative with respect to the second variable y is 1 which is invertible and in the first case we are not sure whether it is.

I have a problem though because in the statement of the implicit function theorem I have, the function needs to be from R^n to R^(n+p) so that we can take the differential of the matrix w.r.t. the p+i variables (i goes from 1 to n). In the hint the function is from R^2 -> R.

Even if that was not a problem I don't know how to end up with the inverse function theorem.

I thank in advance for anyone who is going to help me out :)