Question

Question about proving existence of a function $f$ such that $f \circ f = g$ for an odd function $g$

score 131 · Answer 1 · 2026-02-23 22:24:38

131

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Question about proving existence of a function $f$ such that $f \circ f = g$ for an odd function $g$

Published on 23 Feb 2026 - 22:24

score 24 · Answer 2 · 2020-12-06 19:28:14

24

Views

Power of a relation and a equivalence relation

Published on 06 Dec 2020 - 19:28

score 42 · Answer 3 · 2020-12-07 06:21:44

42

Views

Obtain function from compositions of itself

Published on 07 Dec 2020 - 6:21

score 64 · Answer 4 · 2020-12-10 00:29:34

64

Views

$f \circ g = g \circ f$ $\iff$ $f$ and $g$ are two linear functions?

Published on 10 Dec 2020 - 0:29

score 182 · Answer 5 · 2020-12-19 03:52:26

182

Views

Restriction of two variable function on curve

Published on 19 Dec 2020 - 3:52

score 222 · Answer 6 · 2021-01-05 23:47:46

222

Views

Given functions $h,k:\Bbb R\to \Bbb R$, is it possible to determine whether $f,g:\Bbb R\to\Bbb R$ exist so that $g\circ f=h$ and $f\circ g=k$?

Published on 05 Jan 2021 - 23:47

score 55 · Answer 7 · 2021-01-07 19:35:47

55

Views

If f$(x) = x \arcsin\left(\frac{2x}{1+x^2}\right)$ how can I divide it into a composition of two function like $h(g(x))?$

Published on 07 Jan 2021 - 19:35

score 52 · Answer 8 · 2021-01-07 20:51:51

52

Views

Let $A$ and $B$ be sets; $f: A \times B \rightarrow B \times A$ is given by $f(x,y)=(y,x)$ and $g: B \times A \rightarrow B$ is given by $g(y,x)=y$.

Published on 07 Jan 2021 - 20:51

score 39 · Answer 9 · 2021-01-13 19:39:59

39

Views

Proof that f = {(x,n) e R x Z | n =< x < n + 1} is a function.

Published on 13 Jan 2021 - 19:39

score 45 · Answer 10 · 2021-01-20 17:53:04

45

Views

Example of equivalence relations $S$ and $R$ such that $SR$ is an equivalence relation while $R \cup S$ isn't

Published on 20 Jan 2021 - 17:53

score 38 · Answer 11 · 2021-01-25 03:24:02

38

Views

Is there a way to better write chains of multivariate functions?

Published on 25 Jan 2021 - 3:24

score 152 · Answer 12 · 2021-01-26 19:31:26

152

Views

Composition of inverse trigonometric functions with trigonometric functions

Published on 26 Jan 2021 - 19:31

score 56 · Answer 13 · 2021-02-04 11:28:24

56

Views

Determining an automorphism, when a composition of two automorphisms and the other automorphism is given

Published on 04 Feb 2021 - 11:28

score 53 · Answer 14 · 2021-02-17 01:31:09

53

Views

When is a relation a function in the sets $\mathbb{N},\:\mathbb{Z},\:\mathbb{R}$?

Published on 17 Feb 2021 - 1:31

score 348 · Answer 15 · 2021-02-19 18:24:40

348

Views

Proof that group homomorphisms are associative

Published on 19 Feb 2021 - 18:24

List Question

Question about proving existence of a function $f$ such that $f \circ f = g$ for an odd function $g$

Power of a relation and a equivalence relation

Obtain function from compositions of itself

$f \circ g = g \circ f$ $\iff$ $f$ and $g$ are two linear functions?

Restriction of two variable function on curve

Given functions $h,k:\Bbb R\to \Bbb R$, is it possible to determine whether $f,g:\Bbb R\to\Bbb R$ exist so that $g\circ f=h$ and $f\circ g=k$?

If f$(x) = x \arcsin\left(\frac{2x}{1+x^2}\right)$ how can I divide it into a composition of two function like $h(g(x))?$

Let $A$ and $B$ be sets; $f: A \times B \rightarrow B \times A$ is given by $f(x,y)=(y,x)$ and $g: B \times A \rightarrow B$ is given by $g(y,x)=y$.

Proof that f = {(x,n) e R x Z | n =< x < n + 1} is a function.

Example of equivalence relations $S$ and $R$ such that $SR$ is an equivalence relation while $R \cup S$ isn't

Is there a way to better write chains of multivariate functions?

Composition of inverse trigonometric functions with trigonometric functions

Determining an automorphism, when a composition of two automorphisms and the other automorphism is given

When is a relation a function in the sets $\mathbb{N},\:\mathbb{Z},\:\mathbb{R}$?

Proof that group homomorphisms are associative

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