What does the inverse function say when <mo

Jorden Pace

Jorden Pace

Answered question

2022-06-30

What does the inverse function say when det f ( x ) doesn't equal 0?

Answer & Explanation

alomjabpdl0

alomjabpdl0

Beginner2022-07-01Added 12 answers

I'm assuming you're talking about the inverse function theorem. Basically, if you have a function f : U V where U and V are open sets in Euclidean space, and furthermore, if d e t ( D f ( p ) ) where p U is non-zero, then there is an inverse differentiable function from a neighbourhood of f ( p ) to a neighbourhood of p. Furthermore, the derivative of f 1 at f ( p ) is ( D f ( p ) ) 1 . Intuitively, this says that f is locally invertible (or more interestingly, a local differentiable homeomorphism).

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