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)=x^{2}

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)=x^{2} 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)=x^{2}

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