Question

Suppose that $h : X → Y$ and $f : Z → Y$. Then $\exists g : X → Z$ s.t. $h = f ◦ g$ if $f$ is a bijection.

score 685 · Answer 1 · 2026-03-29 12:26:36

685

Views

Suppose that $h : X → Y$ and $f : Z → Y$. Then $\exists g : X → Z$ s.t. $h = f ◦ g$ if $f$ is a bijection.

Published on 29 Mar 2026 - 12:26

score 52 · Answer 2 · 2022-01-29 14:22:35

52

Views

Find the composition of two relations Rp and Rq

Published on 29 Jan 2022 - 14:22

score 77 · Answer 3 · 2022-01-31 08:10:08

77

Views

Moving a center of a rotation. (Decomposition of a rotation)

Published on 31 Jan 2022 - 8:10

score 238 · Answer 4 · 2022-01-31 14:46:52

238

Views

Continuous function composed with itself is equal to propagation of a differential equation.

Published on 31 Jan 2022 - 14:46

score 199 · Answer 5 · 2026-03-31 10:44:17

199

Views

Any translations can be written in a composition of two half-turns. But, how do we show this?

Published on 31 Mar 2026 - 10:44

score 80 · Answer 6 · 2026-03-31 10:37:56

80

Views

Composition of two rotations with angle $\alpha$ and $-\alpha$, but with different centers is a translation.

Published on 31 Mar 2026 - 10:37

score 74 · Answer 7 · 2026-03-31 12:48:19

74

Views

Any Glide is a product of a Half turn and a Reflection. I have a solution, but I can't understand it.

Published on 31 Mar 2026 - 12:48

score 33 · Answer 8 · 2022-02-07 07:56:58

33

Views

$L: \text{Aff}\left ( \mathbb{R}^n ,\mathbb{R}^n \right ) \to M(n,\mathbb{R})$ is a map of rings?

Published on 07 Feb 2022 - 7:56

score 52 · Answer 9 · 2022-02-22 19:55:25

52

Views

Relations and Cartesian Product: why does $X^1$ differ from $X^0$ and $X^2$?

Published on 22 Feb 2022 - 19:55

score 47 · Answer 10 · 2022-03-11 15:36:19

47

Views

Are the theorems g•f injective/surjective then f/g is injective/surjective invertible?

Published on 11 Mar 2022 - 15:36

score 171 · Answer 11 · 2022-03-25 14:50:16

171

Views

Example of $f,g:\mathbb{R}\to\mathbb{R}$ such that $f\circ g$ is bijective but $g\circ f$ is not bijective

Published on 25 Mar 2022 - 14:50

score 519 · Answer 12 · 2022-03-26 03:19:02

519

Views

How can one find solutions to $f''(x)=f(f(x))$?

Published on 26 Mar 2022 - 3:19

score 142 · Answer 13 · 2022-03-27 00:30:46

142

Views

Decomposing higher order derivatives of composite functions

Published on 27 Mar 2022 - 0:30

score 84 · Answer 14 · 2022-04-19 15:07:57

84

Views

Is composition of reversible functions reversible too?

Published on 19 Apr 2022 - 15:07

score 96 · Answer 15 · 2022-04-28 08:10:49

96

Views

Decompose a function

Published on 28 Apr 2022 - 8:10

List Question

Suppose that $h : X → Y$ and $f : Z → Y$. Then $\exists g : X → Z$ s.t. $h = f ◦ g$ if $f$ is a bijection.

Find the composition of two relations Rp and Rq

Moving a center of a rotation. (Decomposition of a rotation)

Continuous function composed with itself is equal to propagation of a differential equation.

Any translations can be written in a composition of two half-turns. But, how do we show this?

Composition of two rotations with angle $\alpha$ and $-\alpha$, but with different centers is a translation.

Any Glide is a product of a Half turn and a Reflection. I have a solution, but I can't understand it.

$L: \text{Aff}\left ( \mathbb{R}^n ,\mathbb{R}^n \right ) \to M(n,\mathbb{R})$ is a map of rings?

Relations and Cartesian Product: why does $X^1$ differ from $X^0$ and $X^2$?

Are the theorems g•f injective/surjective then f/g is injective/surjective invertible?

Example of $f,g:\mathbb{R}\to\mathbb{R}$ such that $f\circ g$ is bijective but $g\circ f$ is not bijective

How can one find solutions to $f''(x)=f(f(x))$?

Decomposing higher order derivatives of composite functions

Is composition of reversible functions reversible too?

Decompose a function

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