Composition 
Composition[f1,f2,f3,…]
represents a composition of the functions f1, f2, f3, ….
Details

- Composition allows you to build up compositions of functions which can later be applied to specific arguments.
- Composition objects containing Identity or InverseFunction[f] are automatically simplified when possible. »
- Composition has the attributes Flat and OneIdentity.
- Composition can be entered in the form f1 @* f2 @* ….
Examples
open allclose allBasic Examples (2)
Scope (6)
Use pure functions inside Composition:
Use InverseFunction on Composition:
Use Apply with Composition:
Identity inside a composition is simplified:
InverseFunction inside a composition is simplified if possible:
Create a compound operator that looks for symbols and then multiplies them by 2:
Applications (2)
Properties & Relations (7)
Composition composes on the left:
RightComposition composes on the right:
Pure functions let you set up objects that work like Composition:
Different ways of entering compositions:
Compose a function with itself times using Nest:
Compose a function with itself times using RSolve:
Compose TransformationFunction objects:
Use ComposeSeries to do composition of series expansions:
Text
Wolfram Research (1991), Composition, Wolfram Language function, https://reference.wolfram.com/language/ref/Composition.html (updated 2014).
CMS
Wolfram Language. 1991. "Composition." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Composition.html.
APA
Wolfram Language. (1991). Composition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Composition.html