Question

How does a function's smoothness relate to the smoothness of its inverse?

score 94 · Answer 1 · 2026-03-25 09:09:18

94

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How does a function's smoothness relate to the smoothness of its inverse?

Published on 25 Mar 2026 - 9:09

score 179 · Answer 2 · 2020-09-05 21:14:11

179

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Expressing $x = \tan{\frac{u}{2}}$ into a form using $\arctan$ -- Spivak

Published on 05 Sep 2020 - 21:14

score 118 · Answer 3 · 2020-09-07 06:52:15

118

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How to calculate the inverse function of $y=-\frac{1}{2} \ln(1-x^2) \times \text{sign}(x)$?

Published on 07 Sep 2020 - 6:52

score 34 · Answer 4 · 2020-09-07 10:53:23

34

Views

Is $f(x)=(I-\frac{Wxx^TW^T}{\|Wx\|^2})x$ invertible on n-sphere if Jacobian is always non-zero?

Published on 07 Sep 2020 - 10:53

score 761 · Answer 5 · 2026-03-30 10:56:31

761

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Inverse of a convex function

Published on 30 Mar 2026 - 10:56

score 62 · Answer 6 · 2020-09-09 20:11:10

62

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Prove this function is bijective on a domain containing a ball

Published on 09 Sep 2020 - 20:11

score 1.7k · Answer 7 · 2020-09-12 05:30:14

1.7k

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Inverse of product of 2 or more functions

Published on 12 Sep 2020 - 5:30

score 583 · Answer 8 · 2026-03-27 12:07:13

583

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Is there a particular order to doing reflections when there is an inverse reflection (about the line y=x) involved?

Published on 27 Mar 2026 - 12:07

score 3.7k · Answer 9 · 2020-09-15 11:10:53

3.7k

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Let $f(x)=3+x^2+\tan\frac{\pi x}2$, where $-1<x<1$. Find $(f^{-1})'(3)$

Published on 15 Sep 2020 - 11:10

score 261 · Answer 10 · 2020-09-15 12:39:41

261

Views

Derivative of Integral With Limits

Published on 15 Sep 2020 - 12:39

score 179 · Answer 11 · 2026-02-23 01:55:24

179

Views

Closed form of inverse Ackermann function for $kx$, such as $\alpha(kx) = f(k) \alpha(x)$ or $\alpha(kx) < f(k) \alpha(x)$?

Published on 23 Feb 2026 - 1:55

score 83 · Answer 12 · 2020-09-16 04:36:48

83

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Q: What is meant by "invertible on the interval $J=f(\mathbb{R})$?"

Published on 16 Sep 2020 - 4:36

score 57 · Answer 13 · 2020-09-16 15:12:07

57

Views

Find the inverse of $x^2+4x+1, [-2,0)$

Published on 16 Sep 2020 - 15:12

score 43 · Answer 14 · 2020-09-16 19:27:22

43

Views

Q: Proving differentiability at a point for a function based on differentiability of its inverse.

Published on 16 Sep 2020 - 19:27

score 302 · Answer 15 · 2020-09-18 02:14:57

302

Views

How to find the inverse function of $f(x)=\frac x{x-1}$

Published on 18 Sep 2020 - 2:14

List Question

How does a function's smoothness relate to the smoothness of its inverse?

Expressing $x = \tan{\frac{u}{2}}$ into a form using $\arctan$ -- Spivak

How to calculate the inverse function of $y=-\frac{1}{2} \ln(1-x^2) \times \text{sign}(x)$?

Is $f(x)=(I-\frac{Wxx^TW^T}{\|Wx\|^2})x$ invertible on n-sphere if Jacobian is always non-zero?

Inverse of a convex function

Prove this function is bijective on a domain containing a ball

Inverse of product of 2 or more functions

Is there a particular order to doing reflections when there is an inverse reflection (about the line y=x) involved?

Let $f(x)=3+x^2+\tan\frac{\pi x}2$, where $-1<x<1$. Find $(f^{-1})'(3)$

Derivative of Integral With Limits

Closed form of inverse Ackermann function for $kx$, such as $\alpha(kx) = f(k) \alpha(x)$ or $\alpha(kx) < f(k) \alpha(x)$?

Q: What is meant by "invertible on the interval $J=f(\mathbb{R})$?"

Find the inverse of $x^2+4x+1, [-2,0)$

Q: Proving differentiability at a point for a function based on differentiability of its inverse.

How to find the inverse function of $f(x)=\frac x{x-1}$

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