Given a smooth function , if the Jacobian is invertible at 0, then there is a neighborhood containing 0 such that is a diffeomorphism. That is, there is a smooth inverse .

# Inverse Function Theorem

## See also

Diffeomorphism, Implicit Function Theorem, Jacobian
*This entry contributed by Todd
Rowland*

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## Cite this as:

Rowland, Todd. "Inverse Function Theorem." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/InverseFunctionTheorem.html