inverse function theorem (Q931001)
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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
783 × 728; 10 KB
783 × 728; 10 KB
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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Wikipedia(21 entries)
- cawiki Teorema de la funció inversa
- cswiki Věta o inverzní funkci
- dewiki Satz von der Umkehrabbildung
- enwiki Inverse function theorem
- eswiki Teorema de la función inversa
- frwiki Théorème d'inversion locale
- glwiki Teorema da función inversa
- hewiki משפט הפונקציה ההפוכה
- huwiki Inverzfüggvény-tétel
- itwiki Teorema della funzione inversa
- jawiki 逆函数定理
- kowiki 역함수 정리
- nowiki Omvendt funksjonsteorem
- pmswiki Teorema dla fonsion anversa
- ptwiki Teorema da função inversa
- ruwiki Теорема об обратной функции
- svwiki Inversa funktionssatsen
- thwiki ทฤษฎีบทฟังก์ชันผกผัน
- trwiki Ters fonksiyon teoremi
- ukwiki Теорема про обернену функцію
- zhwiki 反函数定理