Section 5.1

Composite Functions

OBJECTIVE 1

Suppose that an oil tanker is leaking oil and we want to be able to determine the area of the circular oil patch around the ship. It is determined that the oil is leaking from the tanker in such a way that the radius of the circular oil patch around the ship is increasing at a rate of 3 feet per minute.

2 3Suppose that 2 3 4 1. Find:f x x g x x

OBJECTIVE 2

2 3Suppose that 2 3 4 1. Find:f x x g x x

1 4 and

4 2f x g x

x x

1Suppose that and 1f x g x x

x

1If 1 and 2 1,show that

2for every in the domain of and .

f x x g x x f g x g f x x

x f g g f

2Find functions and such that if 1f g f g H H x x

2

1Find functions and such that if

2 3f g f g H H x

x