Question

Answered step-by-step

Problem 66 Hard Difficulty

Suppose $ g $ is an odd function and let $ h = f \circ g $. Is $ h $ always an odd function? What if $ f $ is odd? What if $ f $ is even?

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Jeffrey Payo

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Discussion

You must be signed in to discuss.

Top Calculus 3 Educators

Watch More Solved Questions in Chapter 1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Video Transcript

suppose G is an odd function and let h equal f compose with G. And the question is, is each always in our function? What if f is on? And what if f is even? Okay, So I think this question relies entirely on the last two questions. Whether at this odd or at this even so, let's look at a case when f is odd, for example. Okay. And then we'LL let maybe s equal X to the power and where in is hot and odd number So we have a non degree power function Here s o we end up with Oh, and let's ah, let g equal x the power m where and is odd because G is not function as given. Okay, so f complies with G There's going to be s of exit e m where in is odd And now this compass is composition will be excellent m to keep our end in using laws exponents, we have extra m times end and notice that the product m times end if an Izod in Amazon than and the product m times and is on his well, so thus we have S H is our But now we got a look at the second case where f is an even function. Okay. And, um will assume the above except, uh, for N is even function or is even number Then we get half composed with G is X sorry f to the X to power em. This is equal to let me write about eleven more clear And this is X to the M to the power n and lost exponents saying this is exito m times and and know that and plans And if m is he said, And this odd and n is even me and of getting even No. Okay, so why and you know, live in one room so f compose with G is even yeah versus the first case, which we said after both ji Assad. So therefore, to answer the question is each always non function. Therefore, age is not always even or you could say we're on. It all depends on the degree of s or media. If f is even Iran

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 3 Educators

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Kristen Karbon

Calculus 3 Courses

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

James Stewart

Calculus: Early Transcendentals

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Kristen Karbon

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Kristen Karbon

James StewartCalculus: Early Transcendentals

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Kristen Karbon

James Stewart

Calculus: Early Transcendentals