Composite Functions

Given two functions f and g,
the composite function is defined
by the equation
The domain of is the set of all x
in the domain of such that g(x) is
in the domain of f.

Given f(x)=3x + 1 and g(x)= -2x-5
Find a formula for()(x)
find ()(2) and ()(-1)
Find a formula for ()(x)
Find ()(2) and ()(-1)
Does ()(x)=()(x)?

Example
Given and g(x)=x²
Find a formula and the domain for
()(x).

To find the domain of ()(x),
we must find the set of all x in the
domain of g such that g(x) is in the
domain of f.

The domain of g(x)=x² is the set of all
reals. The domain of

is For what values of x is g(x)
in the domain of f?

We need to find the values of x such that

The solution set in this case is
Check the graph of

Given and g(x)=x²
Find a formula and the domain for
()(x).

In this case, you can't just look at the
formula for ()(x) to determine
it's domain.

Example
Given and
Find a formula for ()(x)
Find()(2) and ()(-1)
Find the domain of ()(x)

Example
Given and g(x)=|x|
Find a formula for ()(x) and
()(x), find the domains and
sketch their graphs