Function composition is the nesting of two or more functions to form a single new function. 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, ...].
