 Inverse function theorem

If a continuously differentiable map has invertible derivative at a point, it is a local continuously differentiable diffeomorphism there.

The Inverse Function Theorem is a fundamental result in differential calculus that provides conditions under which a function has a differentiable inverse. It states the following: ### Statement of the Theorem: Let \( f: U \to \mathbb{R}^n \) be a function defined on an open set \( U \subseteq \mathbb{R}^n \). If: 1. \( f \) is continuously differentiable in \( U \), 2.