Operations on Functions
Functions
with overlapping
domains
can be added, subtracted, multiplied and divided. If
and
are two functions, then for all
in the domain of both functions the sum, difference, product and quotient are defined as follows.
Example :
Let
and
Find
and
.
Another way to combine two functions to create a new function is called the
composition of functions
. In the composition of functions we substitute an entire function into another function.
The notation of the function
with
is
and is read
of
of
. It means that wherever there is an
in the function
, it is replaced with the function
. The domain of
is the set of all
in the domain of
such that
is in the domain of
.
Example 1:
Let
and
. Find
.
Example 2:
Let
and
. Find
.
Order DOES matter when finding the composition of functions.
Example 3:
Let
and
.
Find
and
.
Since
.