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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 states that 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. That is, an inverse function exists, in some neighborhood of F(P).

The Jacobian matrix of f^-1 at f(P) is then the inverse of Jf, evaluated at P.

Multivariate calculus

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Topics: Inverse Function Theorem, Inverse Function, Inverse Limit...

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