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.

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 …

Show the composition f(g(x)) f (g (x)) is continuous at a a. My idea: Can I go straight from definition and take δ = min{δ1,δ2} δ = min {δ 1, δ 2}, where δ1 δ 1 is used for the continuity of …

Explore related questions functions asymptotics computational-complexity function-and-relation-composition See similar questions with these tags.

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 ∘ f g ∘ …

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 …

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. …

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 …

May 1, 2019 · The operation of a function depends only on its arguments. Whether you determine what those arguments are directly, or indirectly (through composition) is not the function's …