Apply a composition of functions to arguments:

Apply a composition using infix notation:

Use pure functions inside Composition:

Use Apply with Composition:

Composition objects are automatically simplified when possible:

Assign a Composition object to a variable:

The variable can be used like any other function:

Create a composition of a sequence of functions:

Create a sum of numbers to be displayed in held form:

Composition[f] gives f:

Composition[] gives Identity:

Identity inside a composition is automatically removed:

Consecutive TransformationFunction objects are combined:

InverseFunction of a composition produces a reversed composition of inverse functions:

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 the same composition:

Composition is natural with prefix notation, entering the functions in the same order:

With postfix notation, the functions are reversed relative to pure postfix application:

Compose a function with itself times using Nest:

Compose a function with itself times using RSolve:

Use ComposeSeries to do composition of series expansions:

Composition[…] objects do not hold their arguments:

Use ordinary function application to allow functions to hold their arguments:

Tabulate square roots of values without using auxiliary variables: