Question

Why inverse hyperbolic cosine is just $\ln(x + \sqrt{x^2 - 1})$ and not $\ln(x - \sqrt{x^2 - 1})$ (source: Wikipedia)?

score 153 · Answer 1 · 2026-03-27 18:05:06

153

Views

Why inverse hyperbolic cosine is just $\ln(x + \sqrt{x^2 - 1})$ and not $\ln(x - \sqrt{x^2 - 1})$ (source: Wikipedia)?

Published on 27 Mar 2026 - 18:05

score 89 · Answer 2 · 2023-10-13 01:40:25

89

Views

If a function and its inverse intersect at some point(s), then should there be at least one such point lying on the line y=x?

Published on 13 Oct 2023 - 1:40

score 37 · Answer 3 · 2023-10-13 16:17:16

37

Views

Find the domain of the inverse function

Published on 13 Oct 2023 - 16:17

score 251 · Answer 4 · 2026-03-26 19:10:37

251

Views

How can I solve the equation $y=e^{\cos(x)}\sin(x)$?

Published on 26 Mar 2026 - 19:10

score 378 · Answer 5 · 2023-10-16 02:10:26

378

Views

How do I find the inverse function of $f(x)=\sin(x)+2x+1$

Published on 16 Oct 2023 - 2:10

score 31 · Answer 6 · 2023-10-18 13:04:13

31

Views

What is the mininum perpendicular distance between lines formed from intersection pairs of a function and its inverse

Published on 18 Oct 2023 - 13:04

score 52 · Answer 7 · 2023-10-25 14:34:55

52

Views

Difference between Range and Principal values of trigonometric inverse circular functions.

Published on 25 Oct 2023 - 14:34

score 16 · Answer 8 · 2026-03-09 20:00:53

16

Views

Global inverse given full rank Jacobian (and more)

Published on 09 Mar 2026 - 20:00

score 100 · Answer 9 · 2026-03-26 12:33:41

100

Views

Can an ellipse have integer values for perimeter and area?

Published on 26 Mar 2026 - 12:33

score 18 · Answer 10 · 2023-10-31 15:55:33

18

Views

Density function without the inverse

Published on 31 Oct 2023 - 15:55

score 77 · Answer 11 · 2023-11-05 13:55:58

77

Views

Why isn't the range of cot inverse = (-$\pi/2, \pi/2)$

Published on 05 Nov 2023 - 13:55

score 69 · Answer 12 · 2026-03-27 19:52:46

69

Views

How do I write asinh in terms of $\log$?

Published on 27 Mar 2026 - 19:52

score 137 · Answer 13 · 2023-11-10 21:13:41

137

Views

Solving equations involving inverse trigonometric functions

Published on 10 Nov 2023 - 21:13

score 53 · Answer 14 · 2026-03-26 09:39:57

53

Views

Help with proof of Inverse-Function Theorem in $ \mathbb R ^ n $

Published on 26 Mar 2026 - 9:39

score 102 · Answer 15 · 2026-03-29 05:49:45

102

Views

Show that a biholomorphic map f is conformal

Published on 29 Mar 2026 - 5:49

List Question

Why inverse hyperbolic cosine is just $\ln(x + \sqrt{x^2 - 1})$ and not $\ln(x - \sqrt{x^2 - 1})$ (source: Wikipedia)?

If a function and its inverse intersect at some point(s), then should there be at least one such point lying on the line y=x?

Find the domain of the inverse function

How can I solve the equation $y=e^{\cos(x)}\sin(x)$?

How do I find the inverse function of $f(x)=\sin(x)+2x+1$

What is the mininum perpendicular distance between lines formed from intersection pairs of a function and its inverse

Difference between Range and Principal values of trigonometric inverse circular functions.

Global inverse given full rank Jacobian (and more)

Can an ellipse have integer values for perimeter and area?

Density function without the inverse

Why isn't the range of cot inverse = (-$\pi/2, \pi/2)$

How do I write asinh in terms of $\log$?

Solving equations involving inverse trigonometric functions

Help with proof of Inverse-Function Theorem in $ \mathbb R ^ n $

Show that a biholomorphic map f is conformal

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