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I'm trying to find out the difference between the implicit function theorem and the inverse function theorem. One of the obstacles of my understanding, is that I can't find a function that it globally locally not invertible but does have an implicit form.

Meaning: find an example, which I can use the implicit theorem globally, but I can't use the inverse function even at one point.

Thanks.

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  • $\begingroup$ The implicit and inverse function theorems, as they're usually stated are purely local existence theorems. In fact, they're equivalent to one another (if you assume one of them is true, you can prove the other one) $\endgroup$ – peek-a-boo Apr 25 at 20:58

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