Question

The function $g(x)=3x+\ln2x$ for $x>0$. Find $g'(x)$ and prove that $g(x)$ has an inverse function.

score 185 · Answer 1 · 2018-12-08 21:38:15

185

Views

The function $g(x)=3x+\ln2x$ for $x>0$. Find $g'(x)$ and prove that $g(x)$ has an inverse function.

Published on 08 Dec 2018 - 21:38

score 210 · Answer 2 · 2018-12-10 10:57:04

210

Views

Find Random Number Generator following the density $f (x) = \frac{1 + \alpha x}{2}$, $ −1 ≤ x ≤ 1$, $−1 ≤\alpha ≤ 1$

Published on 10 Dec 2018 - 10:57

score 82 · Answer 3 · 2018-12-10 11:21:54

Simplified form of $\cos^{-1}\big[\frac{3}{5}\cdot\cos x+\frac{4}{5}\cdot\sin x\big]$, where $x\in\big[\frac{-3\pi}{4},\frac{3\pi}{4}\big]$

score 5.1k · Answer 4 · 2018-12-10 23:39:17

5.1k

Views

If $f(x)=\int_{3}^x \sqrt{1+t^3} dt$ Find $(f^{-1})'(0)$

Published on 10 Dec 2018 - 23:39

score 187 · Answer 5 · 2018-12-11 18:53:24

187

Views

Find the value of $3\tan^{-1}\frac{1}{2}+2\tan^{-1}\frac{1}{5}+\sin^{-1}\frac{142}{65\sqrt{5}}$

Published on 11 Dec 2018 - 18:53

score 32 · Answer 6 · 2026-03-25 04:43:49

32

Views

Is this pair of equations impossible to solve for x? $y_1 = x_2 - v^{\pm 1}e^{-x_1}$, or equivalently $(x - y)c^{\exp(-x)} = z$

Published on 25 Mar 2026 - 4:43

score 1.4k · Answer 7 · 2018-12-15 05:24:26

1.4k

Views

Sum of $50$ terms of $\cot^{-1}3+\cot^{-1}7+\cot^{-1}13+\cot^{-1}21+.....$

Published on 15 Dec 2018 - 5:24

score 289 · Answer 8 · 2018-12-15 10:08:26

289

Views

Looking for a simple interpretation

Published on 15 Dec 2018 - 10:08

score 54 · Answer 9 · 2018-12-15 12:37:56

54

Views

Inverse of function and derivative

Published on 15 Dec 2018 - 12:37

score 120 · Answer 10 · 2018-12-16 20:45:58

120

Views

Greater of the angles $\alpha=2\tan^{-1}(2\sqrt{2}-1)$, $\beta=3\sin^{-1}\frac{1}{3}+\sin^{-1}\frac{3}{5}$

Published on 16 Dec 2018 - 20:45

score 206 · Answer 11 · 2018-12-18 09:28:46

206

Views

sum of the infinite series $\cot^{-1}(2.1^2)+\cot^{-1}(2.2^2)+\cot^{-1}(2.3^2)+\cot^{-1}(2.4^2)+...$

Published on 18 Dec 2018 - 9:28

score 1.4k · Answer 12 · 2018-12-19 08:53:33

1.4k

Views

Find the value of $\cot^{-1}21+\cot^{-1}13+\cot^{-1}(-8)$

Published on 19 Dec 2018 - 8:53

score 61 · Answer 13 · 2026-03-25 07:50:08

61

Views

Inverse Function Theorem (Domain, one-to-one, application)

Published on 25 Mar 2026 - 7:50

score 444 · Answer 14 · 2018-12-19 22:21:23

444

Views

If F is a homomorphism function, i want to ask the inverse of F is also homomorphism?

Published on 19 Dec 2018 - 22:21

score 278 · Answer 15 · 2018-12-21 18:37:24

278

Views

How to calculate the inverse of $\mathbb{R}^2$-version of the inverse Cayley map

Published on 21 Dec 2018 - 18:37

List Question

The function $g(x)=3x+\ln2x$ for $x>0$. Find $g'(x)$ and prove that $g(x)$ has an inverse function.

Find Random Number Generator following the density $f (x) = \frac{1 + \alpha x}{2}$, $ −1 ≤ x ≤ 1$, $−1 ≤\alpha ≤ 1$

Simplified form of $\cos^{-1}\big[\frac{3}{5}\cdot\cos x+\frac{4}{5}\cdot\sin x\big]$, where $x\in\big[\frac{-3\pi}{4},\frac{3\pi}{4}\big]$

If $f(x)=\int_{3}^x \sqrt{1+t^3} dt$ Find $(f^{-1})'(0)$

Find the value of $3\tan^{-1}\frac{1}{2}+2\tan^{-1}\frac{1}{5}+\sin^{-1}\frac{142}{65\sqrt{5}}$

Is this pair of equations impossible to solve for x? $y_1 = x_2 - v^{\pm 1}e^{-x_1}$, or equivalently $(x - y)c^{\exp(-x)} = z$

Sum of $50$ terms of $\cot^{-1}3+\cot^{-1}7+\cot^{-1}13+\cot^{-1}21+.....$

Looking for a simple interpretation

Inverse of function and derivative

Greater of the angles $\alpha=2\tan^{-1}(2\sqrt{2}-1)$, $\beta=3\sin^{-1}\frac{1}{3}+\sin^{-1}\frac{3}{5}$

sum of the infinite series $\cot^{-1}(2.1^2)+\cot^{-1}(2.2^2)+\cot^{-1}(2.3^2)+\cot^{-1}(2.4^2)+...$

Find the value of $\cot^{-1}21+\cot^{-1}13+\cot^{-1}(-8)$

Inverse Function Theorem (Domain, one-to-one, application)

If F is a homomorphism function, i want to ask the inverse of F is also homomorphism?

How to calculate the inverse of $\mathbb{R}^2$-version of the inverse Cayley map

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