We speak of a composite of two functions when:
- two functions map the value for each other
or
- the range of one function represents the domain of another function.
Let's look at the composite in the sketch:
Composite of functions 
and 
From the figure we can see that the function maps 
(from the set 
) to 
(to the set 
) and then immediately maps to the function to 
(in the set ).
Note that the range of the function is the domain of the function .
Mathematically, we write the mapping of the function :
and functions
The composite of the functions and is the function 
, which adapts the images 
in the set to the element from the set :
We can also notice that we use two names for the composite: 
can also be written as .
