A General Implicit/Inverse Function Theorem

TL;DR

This paper introduces a unified Implicit/Inverse Function Theorem that generalizes both classical theorems, allowing for easier derivation and understanding of their relationship.

Contribution

It presents a generalized theorem that encompasses both the Implicit and Inverse Function Theorems, simplifying their derivation and connection.

Findings

Unified theorem derived from classical theorems

Simplifies understanding of implicit and inverse functions

Facilitates easier derivation of related theorems

Abstract

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized version.