There are so many real-world examples of this it's hard to pick one. Basically any time you are doing one computation and then doing another computation, that is composition of functions.

Jul 24, 2018 · It doesn't cause confusion because the function being talked about is quite straightforward. But I'm still interested in knowing what the "correct" way/s to describe $g \circ …

Jul 17, 2015 · The standard definition (say from Wolfram) is in fact the second one. Also, the standard definition allows the range of the function to be a subset of the stated codomain. …

Jun 13, 2012 · In fact, matrix multiplication is defined the (somewhat strange) way it is precisely so that it corresponds to composition of linear transformations.

Dec 26, 2021 · calculus limits functions function-and-relation-composition Share Cite edited Dec 27, 2021 at 4:07

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.

In particular, it gives the formula for a for the Fourier transform of a composition. Since RT^ R T ^ is a composition of linear functions, it is linear. Thus, to understand RT^ R T ^ it suffices to …

Apr 3, 2018 · 2 The standard notation in my area of interest (fractal geometry and analysis on fractals) is to use superscript notation for functional composition. This is not unreasonable, as …

Feb 12, 2023 · The function of the limit is not guaranteed to be the limit of the function generally speaking. Pragmatically, if the right and left limits approach the same finite value in the …

Is there a commonly-accepted operator which defines multiple function composition? I have not been able to find one on any of the related Wikipedia pages. In one of my proofs, I've been …