The nesting of two or more functions to form a single new function is known as function composition. The composition
of two functions 
and 
is denoted 
,
where the domain of 
includes the range of 
. The notation
 |
is sometimes used to explicitly indicate the variable.
Function composition is associative, so that
 |
If the function 
is continuous at 
and 
is continuous at 
, then 
is also continuous
at 
.
A function 
which is the composition of two other functions, say 
and 
, is sometimes said to be a composite function.
Faà di Bruno's formula gives an explicit formula for the 
th
derivative of the composition 
.
Function composition is implemented in the Wolfram Language as Composition[f1, f2, ...].
