List questions from function-and-relation-composition

Published on 27 Mar 2026 - 16:47

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What are the procedures to analyze the similarity of graphs?

Published on 29 Mar 2023 - 14:40

91

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$f(n) = \frac{n^2 + n + 4}{2}, g(f(n)) = f(g(n))$ such that $g(n)$ is an integer.

Published on 23 Feb 2026 - 12:08

71

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Let $f:[0,1]\to \mathbb{R},f(x)=4x(1-x),f_n(x)=f(f_{n-1}(x))\;\forall n\geq 1$ and $f_0(x)=x$. Find number of solutions to the equation $f_n(x)=x$.

Published on 17 Apr 2023 - 15:12

75

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Limit of a composition function exists, but limit of the outer function does not exists

Published on 23 Apr 2023 - 11:58

108

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Expected value of a random composition of functions

Published on 04 May 2023 - 6:30

27

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Functions that preserve the minimum inside an integral

Published on 05 May 2023 - 12:38

82

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Under what conditions is $f = g^2$ convex?

Published on 09 May 2023 - 8:24

70

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Let the functions $f$, $g$ and $h$ be given, compute $(f \circ g \circ h)(4)$

Published on 11 May 2023 - 5:48

24

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Vector-valued function composition

Published on 14 May 2023 - 14:26

126

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If $h:[0,1]\to [0,1]$ is continuous and surjective, then does there exist a continuous function $f$ such that $ff=h?$ If so, is $f$ unique?

Published on 21 May 2023 - 22:15

26

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Low rank function decomposition — necessary and sufficient conditions

Published on 27 Mar 2026 - 8:40

161

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Is $f(g(x))$ discontinuous?

Published on 23 May 2023 - 17:42

57

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How to intuitively think about composition of relations?

Published on 27 May 2023 - 12:04

165

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Show that if $g\circ f$ is injective, then $f$ must be injective. Is it true that $g$ must also be injective?

Published on 31 May 2023 - 14:36

List Question

Prove that $\tanh (\cosh^{-1} (x)) = \frac{\sqrt{x^2-1}}{x}$

What are the procedures to analyze the similarity of graphs?

$f(n) = \frac{n^2 + n + 4}{2}, g(f(n)) = f(g(n))$ such that $g(n)$ is an integer.

Let $f:[0,1]\to \mathbb{R},f(x)=4x(1-x),f_n(x)=f(f_{n-1}(x))\;\forall n\geq 1$ and $f_0(x)=x$. Find number of solutions to the equation $f_n(x)=x$.

Limit of a composition function exists, but limit of the outer function does not exists

Expected value of a random composition of functions

Functions that preserve the minimum inside an integral

Under what conditions is $f = g^2$ convex?

Let the functions $f$, $g$ and $h$ be given, compute $(f \circ g \circ h)(4)$

Vector-valued function composition

If $h:[0,1]\to [0,1]$ is continuous and surjective, then does there exist a continuous function $f$ such that $ff=h?$ If so, is $f$ unique?

Low rank function decomposition — necessary and sufficient conditions

Is $f(g(x))$ discontinuous?

How to intuitively think about composition of relations?

Show that if $g\circ f$ is injective, then $f$ must be injective. Is it true that $g$ must also be injective?

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