inverse function theorem (Q6482806)
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theorem that, if a function is continuously differentiable with nonzero Jacobian determinant at a given point, then it is locally invertible near that point
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | inverse function theorem |
theorem that, if a function is continuously differentiable with nonzero Jacobian determinant at a given point, then it is locally invertible near that point |
Statements
Inv-Fun-Thm-3.png
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a counterexample demonstrating the necessity of continuous differentiability in the inverse function theorem: the function 𝑥+2𝑥²sin(¹⁄𝑥) is differentiable (but not continuously so) at 0 and does not admit a local inverse near 0 (English)
kontraŭekzemplo pri la neceso de kontinua derivebleco en la funkcio de la inversa funkcio: la funkcio 𝑥+2𝑥²sin(¹⁄𝑥) estas derivebla (sed ne kontinue derivebla) ĉe 0, kaj loka inversa funkcio mankas ĉirkaŭ 0 (Esperanto)
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Identifiers
43987214
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inverse function theorem
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InverseFunctionTheorem
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