Problem

The Bessel function of order 0, $ y = J (x), $ sa…

01:39

Problem 78 Hard Difficulty

(a) Show that $ f(x) = x + r^x $ is one-to-one.
(b) What is the value of $ f^{-1}(1)? $
(c) Use the formula from Exercise 77(a) to find $ (f^{-1})'(1). $

Answer

(a)Please see proof.
(b) $$
f^{-1}(1)=0
$$
(c) $$
\frac{1}{2}
$$

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Watch More Solved Questions in Chapter 3

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

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Video Transcript

in this problem, we're given a function of black sort of perfect explosive. Each X in front 81 short at this punch. One hole. Let's say, uh, look at first, they were job dysfunction. That final thanks. That is one plus X. Well, let's look at the second derivative. And this each of the eggs 37 10 would be the JD X, and you would get the same behavior for all fire order. There it is. So for any value of X, we know that each of the eggs will be positive, meaning that all the derivatives will be positive. So it means that dysfunction is increasing always since that is always increasing. Increasing this function is 12 or all right park years front. Yours or no, let's say that, um oh, um, that's is so f universe. Let's write it this time instead of f universe off X plus, each of eggs is equal. Thanks. We want an X plus, you two x to be one. If that is born, we see that X should zero, and that is the answer. So we consider a f in worse off one is unequalled zero. All right, import CVS, But English front or beginning used the question that we drive in problem 77 Soviet. Oh, that f inwards Prime off exit was born over f crime of immerse effects. So that is more over a probable and universal one in part. Maybe find FT merciful as zero. So that is warm or prime. Zero. What? Is that a problem? Zero. We know that prime effects from A is equal to one plus you to the ex that primary zero would be born boss Jiro And that is due so that the answer would be, um, dinner's prime one. Is it on over to?

Doruk I.

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Problem

The Bessel function of order 0, $ y = J (x), $ sa…

Problem 78 Hard Difficulty

(a) Show that $ f(x) = x + r^x $ is one-to-one.
(b) What is the value of $ f^{-1}(1)? $
(c) Use the formula from Exercise 77(a) to find $ (f^{-1})'(1). $

Answer

(a)Please see proof.
(b) $$
f^{-1}(1)=0
$$
(c) $$
\frac{1}{2}
$$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Problem

The Bessel function of order 0, $ y = J (x), $ sa…

Problem 78 Hard Difficulty

(a) Show that $ f(x) = x + r^x $ is one-to-one.(b) What is the value of $ f^{-1}(1)? $(c) Use the formula from Exercise 77(a) to find $ (f^{-1})'(1). $

Answer

(a)Please see proof.(b) $$f^{-1}(1)=0$$(c) $$\frac{1}{2}$$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

(a) Show that $ f(x) = x + r^x $ is one-to-one.
(b) What is the value of $ f^{-1}(1)? $
(c) Use the formula from Exercise 77(a) to find $ (f^{-1})'(1). $

(a)Please see proof.
(b) $$
f^{-1}(1)=0
$$
(c) $$
\frac{1}{2}
$$