Given two functions f and
g,we can form a new function as follows: start with
an input value x in the domain of g and find the corresponding output
value g(x). If the number g(x) is in the domain of f, we can then
find the output value of f at g(x). That is, we can find the value f(g(x)).
This process is called composition of functions. See figure 1 below.
for any two functions f and g, the composite function is
domain of is the set of all
numbers, x, in the domain of g for which g(x) is in the domain of
find the domain of the
composite function .
the domain of , we first notice that
the domain of g is
and the domain of f is
Thus, g(x) cannot equal
0. So we solve the equation
We must exclude -3 from
the domain of . The domain of
To check our answer, we can find the composite function
We see that is