List questions from function-and-relation-composition

Published on 25 Mar 2026 - 12:06

280

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«A cycle is a product of transpositions» $\iff$ «Rearrangement of $n$ objects is the same as successively interchanging pairs»

Published on 19 Mar 2026 - 18:34

70

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Is this composition of functions $h(x)=\begin{cases}f(x)& -1\leq x\leq 0,\\g(x), &\;\;\;\;\;\;\;\;\;x>0\end{cases}$ continuous?

Published on 24 Mar 2026 - 10:39

68

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If $φ: A → B$ and $ψ: B → C$ are homomorphisms, then $ψ \circ φ: A → C$ is a homomorphism.

Published on 25 Mar 2026 - 1:18

28

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A question about finding the inverse of a function

Published on 24 Mar 2026 - 16:07

376

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Is there a standard notation for the pre-composition operator?

Published on 25 Mar 2026 - 1:29

6.1k

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Limit of composite functions

Published on 24 Mar 2026 - 14:56

276

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Unable to understand how to solve piecewise composition of two functions

Published on 24 Mar 2026 - 17:33

166

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Rank of composition of non-square transpose matrices

Published on 25 Mar 2026 - 2:39

1.2k

Views

Mapping non-convex functions onto convex functions

Published on 24 Mar 2026 - 22:35

344

Views

Rigorous definition of iteration of logarithm

Published on 24 Mar 2026 - 20:39

36

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Proof that a sequence of numbers must always contain a perfect square

Published on 25 Mar 2026 - 0:27

2.1k

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Identity function

Published on 25 Mar 2026 - 3:20

104

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What must $f$ satisfy in order to conclude $h \circ f=g \circ f \Rightarrow h = g$

Published on 24 Mar 2026 - 22:50

555

Views

Restrictions of compositions

Published on 25 Mar 2026 - 0:29

List Question

Composition of Relations (functions)

«A cycle is a product of transpositions» $\iff$ «Rearrangement of $n$ objects is the same as successively interchanging pairs»

Is this composition of functions $h(x)=\begin{cases}f(x)& -1\leq x\leq 0,\\g(x), &\;\;\;\;\;\;\;\;\;x>0\end{cases}$ continuous?

If $φ: A → B$ and $ψ: B → C$ are homomorphisms, then $ψ \circ φ: A → C$ is a homomorphism.

A question about finding the inverse of a function

Is there a standard notation for the pre-composition operator?

Limit of composite functions

Unable to understand how to solve piecewise composition of two functions

Rank of composition of non-square transpose matrices

Mapping non-convex functions onto convex functions

Rigorous definition of iteration of logarithm

Proof that a sequence of numbers must always contain a perfect square

Identity function

What must $f$ satisfy in order to conclude $h \circ f=g \circ f \Rightarrow h = g$

Restrictions of compositions

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