In mathematics, 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 a point P a function f:Rn-->Rn has a Jacobian determinant that is nonzero, and F is continuously differentiable near P, it is an invertible function near P.
The Jacobian matrix of f-1 at f(P) is then the inverse of Jf, evaluated at P.