Download ppt - Sulpcegu5e ppt 5_1

Transcript
Page 1: Sulpcegu5e ppt 5_1

Section 5.1

Composite Functions

Page 2: Sulpcegu5e ppt 5_1

OBJECTIVE 1

Page 3: Sulpcegu5e ppt 5_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.

Page 4: Sulpcegu5e ppt 5_1
Page 5: Sulpcegu5e ppt 5_1
Page 6: Sulpcegu5e ppt 5_1

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

Page 7: Sulpcegu5e ppt 5_1

OBJECTIVE 2

Page 8: Sulpcegu5e ppt 5_1

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

Page 9: Sulpcegu5e ppt 5_1

1 4 and

4 2f x g x

x x

Page 10: Sulpcegu5e ppt 5_1

1Suppose that and 1f x g x x

x

Page 11: Sulpcegu5e ppt 5_1

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

Page 12: Sulpcegu5e ppt 5_1
Page 13: Sulpcegu5e ppt 5_1

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

Page 14: Sulpcegu5e ppt 5_1

2

1Find functions and such that if

2 3f g f g H H x

x