Question

If $A,B\in\mathcal{B}(\mathcal{H}):AB=BA$ and $A$ does not have an inverse, then $AB$ does not have an inverse

score 47 · Answer 1 · 2023-05-10 13:32:39

If $A,B\in\mathcal{B}(\mathcal{H}):AB=BA$ and $A$ does not have an inverse, then $AB$ does not have an inverse

Published on 10 May 2023 - 13:32

score 110 · Answer 2 · 2023-05-11 11:18:42

(SOLVED) Simplify $\cos^{-1}\left( \frac{7}{2}\left( 1+\cos{2x} \right) + \sqrt{\left( \sin^{2}{x} - 48\cos^{2}{x} \right)}\sin{x}\right)$

score 54 · Answer 3 · 2023-05-13 04:36:44

54

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Difficult simplification Inverse function

Published on 13 May 2023 - 4:36

score 45 · Answer 4 · 2026-03-29 05:12:10

45

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If $y=f(x)$ such that $(x+1)^3+(y+1)^3=16$ then evaluate : $\frac{d}{dx}\left(f(x+g(x)).g(x+f(x))\right)$ at $x=-1+\sqrt[3]{15}$

Published on 29 Mar 2026 - 5:12

score 101 · Answer 5 · 2023-05-21 21:39:53

101

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Finding an inverse for Clausen Functions

Published on 21 May 2023 - 21:39

score 88 · Answer 6 · 2023-05-23 16:24:39

88

Views

What sort of applications are there for $(dy/dx) (dx/dy) = 1$?

Published on 23 May 2023 - 16:24

score 118 · Answer 7 · 2026-03-27 02:38:07

118

Views

Inverse of a gamma function

Published on 27 Mar 2026 - 2:38

score 95 · Answer 8 · 2023-06-10 16:08:30

95

Views

Proving $\arctan(\sinh(x))= 2\arctan(e^x) - \frac{\pi}{2}$

Published on 10 Jun 2023 - 16:08

score 51 · Answer 9 · 2023-06-17 23:21:02

51

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Are these two series of the arctangent function the same?

Published on 17 Jun 2023 - 23:21

score 21 · Answer 10 · 2023-06-19 11:22:24

21

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Inverting the sum of two inverses of integrals of strictly positive functions

Published on 19 Jun 2023 - 11:22

score 56 · Answer 11 · 2023-06-20 13:51:30

56

Views

Is there a single-valued function linear in $\sin(x)$ and $\cos(x)$ that is invertible on $[-\pi, \pi)$ or $[0,2\pi)$?

Published on 20 Jun 2023 - 13:51

score 99 · Answer 12 · 2026-03-28 02:42:48

99

Views

Implicit Inverse function Theorems on $\mathbb R^2$ and injective functions

Published on 28 Mar 2026 - 2:42

score 48 · Answer 13 · 2026-03-26 04:34:55

48

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Let $f(x)=x^2+3x-3,x\gt0.$ If $n$ points $x_1,x_2,...,x_n$ are chosen on the x-axis, evaluate $\frac{x_1+x_2+...+x_n}n$

Published on 26 Mar 2026 - 4:34

score 118 · Answer 14 · 2023-06-27 15:58:42

118

Views

Why is not $\,f(x)=\arcsin\left(2x\sqrt{1 - x^2}\right)$ a one to one function?

Published on 27 Jun 2023 - 15:58

score 129 · Answer 15 · 2026-03-28 11:35:23

129

Views

Does $f(x)=x$ and $f(f(x))=x$ have exactly the same set of solutions when $f(x)$ is monotone?

Published on 28 Mar 2026 - 11:35

List Question

If $A,B\in\mathcal{B}(\mathcal{H}):AB=BA$ and $A$ does not have an inverse, then $AB$ does not have an inverse

(SOLVED) Simplify $\cos^{-1}\left( \frac{7}{2}\left( 1+\cos{2x} \right) + \sqrt{\left( \sin^{2}{x} - 48\cos^{2}{x} \right)}\sin{x}\right)$

Difficult simplification Inverse function

If $y=f(x)$ such that $(x+1)^3+(y+1)^3=16$ then evaluate : $\frac{d}{dx}\left(f(x+g(x)).g(x+f(x))\right)$ at $x=-1+\sqrt[3]{15}$

Finding an inverse for Clausen Functions

What sort of applications are there for $(dy/dx) (dx/dy) = 1$?

Inverse of a gamma function

Proving $\arctan(\sinh(x))= 2\arctan(e^x) - \frac{\pi}{2}$

Are these two series of the arctangent function the same?

Inverting the sum of two inverses of integrals of strictly positive functions

Is there a single-valued function linear in $\sin(x)$ and $\cos(x)$ that is invertible on $[-\pi, \pi)$ or $[0,2\pi)$?

Implicit Inverse function Theorems on $\mathbb R^2$ and injective functions

Let $f(x)=x^2+3x-3,x\gt0.$ If $n$ points $x_1,x_2,...,x_n$ are chosen on the x-axis, evaluate $\frac{x_1+x_2+...+x_n}n$

Why is not $\,f(x)=\arcsin\left(2x\sqrt{1 - x^2}\right)$ a one to one function?

Does $f(x)=x$ and $f(f(x))=x$ have exactly the same set of solutions when $f(x)$ is monotone?

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