Inverse function theorem

The Inverse Function Theorem gives sufficient conditions for a vector valued function to be invertible on an open region containing a point in its domain.

The Theorem:

If at p f:Rn-->Rn has a Jacobian determinant that is nonzero, it is an invertible function near p.

The Jacobian matrix of f-inverse at f(p) is the inverse of Jf, evaluated at f(p).