Question

Does $f(x) = x - \tanh(x)$ have an inverse function that can be expressed in terms of elementary functions?

score 273 · Answer 1 · 2026-03-25 14:27:06

273

Views

Does $f(x) = x - \tanh(x)$ have an inverse function that can be expressed in terms of elementary functions?

Published on 25 Mar 2026 - 14:27

score 192 · Answer 2 · 2020-01-23 22:22:16

192

Views

Intuitive Explanation of Hyperbolic Functions and Relationship to Euler’s Formula

Published on 23 Jan 2020 - 22:22

score 875 · Answer 3 · 2020-01-24 10:20:51

875

Views

What substitution is needed to show that $\int \frac{1}{\sqrt{x^2+a^2}}\,dx=\sinh^{-1} \left( \frac{x}{a} \right) +C $?

Published on 24 Jan 2020 - 10:20

score 411 · Answer 4 · 2020-01-25 14:49:20

411

Views

Prove $~\cosh x > x~,~ \forall x~$

Published on 25 Jan 2020 - 14:49

score 1.5k · Answer 5 · 2020-01-26 09:00:13

1.5k

Views

Calculating Fourier Transform of Sech(x)

Published on 26 Jan 2020 - 9:00

score 50 · Answer 6 · 2026-02-23 04:33:48

50

Views

How does one derive the Lorentz transform for rectangular hyperbolas?

Published on 23 Feb 2026 - 4:33

score 65 · Answer 7 · 2020-01-28 08:29:40

65

Views

Why does the distance between approach $\ln(2)$ as y increases?

Published on 28 Jan 2020 - 8:29

score 647 · Answer 8 · 2020-01-30 13:27:45

How to transform the $\tanh$ sigmoid function so that it starts from $f(0)=0$, goes asymptotically to $1$, and has $f(0.1)=a$ and $f(0.9)=b$?

score 220 · Answer 9 · 2020-01-30 23:51:48

220

Views

Using the Residue Theorem to Evaluate Contour Integrals

Published on 30 Jan 2020 - 23:51

score 282 · Answer 10 · 2020-02-03 03:26:13

282

Views

Why is $\cosh$ used in parametrization of $x^2-y^2=1$ when $\cosh$ can't be negative?

Published on 03 Feb 2020 - 3:26

score 227 · Answer 11 · 2026-03-26 02:56:10

227

Views

Verify the closed form of $\sum_{k=1}^{\infty}\frac{\coth\pi k}{ke^{\pi k}}$

Published on 26 Mar 2026 - 2:56

score 78 · Answer 12 · 2020-02-04 19:48:33

78

Views

Implicit function defined via transcendental equation

Published on 04 Feb 2020 - 19:48

score 124 · Answer 13 · 2020-02-08 21:59:52

124

Views

What is the difference between an exponential func. and a hyperbolic secant func.?

Published on 08 Feb 2020 - 21:59

score 328 · Answer 14 · 2020-02-11 07:51:48

328

Views

Conditions for intersection of two functions

Published on 11 Feb 2020 - 7:51

score 505 · Answer 15 · 2020-02-16 18:56:12

505

Views

Proof $ \cosh x=1 \Leftrightarrow x=0 $

Published on 16 Feb 2020 - 18:56

List Question

Does $f(x) = x - \tanh(x)$ have an inverse function that can be expressed in terms of elementary functions?

Intuitive Explanation of Hyperbolic Functions and Relationship to Euler’s Formula

What substitution is needed to show that $\int \frac{1}{\sqrt{x^2+a^2}}\,dx=\sinh^{-1} \left( \frac{x}{a} \right) +C $?

Prove $~\cosh x > x~,~ \forall x~$

Calculating Fourier Transform of Sech(x)

How does one derive the Lorentz transform for rectangular hyperbolas?

Why does the distance between approach $\ln(2)$ as y increases?

How to transform the $\tanh$ sigmoid function so that it starts from $f(0)=0$, goes asymptotically to $1$, and has $f(0.1)=a$ and $f(0.9)=b$?

Using the Residue Theorem to Evaluate Contour Integrals

Why is $\cosh$ used in parametrization of $x^2-y^2=1$ when $\cosh$ can't be negative?

Verify the closed form of $\sum_{k=1}^{\infty}\frac{\coth\pi k}{ke^{\pi k}}$

Implicit function defined via transcendental equation

What is the difference between an exponential func. and a hyperbolic secant func.?

Conditions for intersection of two functions

Proof $ \cosh x=1 \Leftrightarrow x=0 $

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