It is obvious that function composition is/(must be) associative, but attempts at modest generalization, leave me questioning where, if anywhere, there might be a bit of sleight of hand. It would be fun to have a long thoughtful discussion leading to the agreement that indeed all the matters at are trivially obvious, obviously trivial, and that ...

$\begingroup$ Is it possible for a (lowest terms) rational function with a numerator or denominator of degree greater than 1 to have finite order under composition? You prove something like that is impossible when finding the automorphisms of k[x] or k(x) or whatever. $\endgroup$

Let $T(S)$ be the set of all functions on $S = \\{1,2,3 \\}$. Show that $T(S)$ is a group under composition of functions. I am to prove that this is either true or ...

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function-and-relation-composition; Share. Cite. Follow edited Oct 16, 2013 at 1:28. dfeuer. 9,279 3 3 gold ...

Aug 19, 2017 · Which look just like two by two matrices over $\mathbb{K}$ modulo scalar matrices. And this works well for what you want them to do, since if you check then $\frac{ax+0}{0x+a}$ (a function relating to a scalar matrix and the projective function [aX + 0Y: 0X + aY] = [X:Y]) is indeed the identity function.

Have a look at Bergner et al. 2006 "A Spectral Analysis of Function Composition and Its Implications for Sampling in Direct Volume Visualization" IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 12, NO. 5. Sec. 3. Unfortunately, it's not quite as simple as the transform of a convolution or even the derivative.

Jan 22, 2025 · $\begingroup$ A matrix is a way to represent a linear function, and the formula for matrix multiplication arises from the matrix representation of the composition of two such functions. It’s unfortunate that this is not emphasized in your precalculus course. $\endgroup$

function-and-relation-composition; Share. Cite. Follow edited Nov 29, 2021 at 3:43. u243676. 115 5 5 ...

Mar 12, 2024 · Confusion about function composition. Ask Question Asked 10 months ago. Modified 10 months ago. Viewed 102 ...