Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Concept explainers

Exponential Growth Model
The relation that represents an exponential function is:
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Question
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Chapter 1.6, Problem 107E
To determine

To find : the value of function.

Expert Solution & Answer
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Answer to Problem 107E

The value of function (f−1of−1)(−6) is −168.

Explanation of Solution

Given information :

The functions are f(x)=18x−3 and g(x)=x3.

The function for finding value (f−1of−1)(−6).

Calculation : to find the value of function, it is needed to first find the inverse functions of f(x) and g(x).

To find the inverse function of f(x) , substitute f(x)=y in the function,

  f(x)=18x−3y=18x−3          [substitute f(x)=y]18x=y+3          [add 3 both side]x=8y+24        [multiply by 8]f−1(x)=8x+24    [simplify]

To find the inverse function of g(x) , substitute g(x)=y in the function,

  g(x)=x3y=x3           [substitute g(x)=y]x=y3           [cube root]g−1(x)=x3    [simplify]

Now to find the value of function (f−1of−1)(−6) , substitute x=−6 ,

  (f−1of−1)(−6)=f−1(f−1(−6))(f−1of−1)(−6)=f−1(8(−6)+24)         [substitue x=−6 in f(x)=8x+24](f−1of−1)(−6)=f−1(−24)            [multiply and subtract](f−1of−1)(−6)=8(−24)+24          [substitute x=−24 in f(x)=8x+24](f−1of−1)(−6)=−168                   [simplify]

Thus, The value of function (f−1of−1)(−6) is −168.

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Chapter 1.6, Problem 106E
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Chapter 1.6, Problem 108E

Chapter 1 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.1 - Prob. 3ECh. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - Prob. 10E
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Prob. 120ECh. 1.6 - Prob. 121ECh. 1.6 - Prob. 122ECh. 1.6 - Prob. 123ECh. 1.6 - Prob. 124ECh. 1.6 - Prob. 125ECh. 1.6 - Prob. 126ECh. 1.6 - Prob. 127ECh. 1.6 - Prob. 128ECh. 1.6 - Prob. 129ECh. 1.6 - Prob. 130ECh. 1.6 - Prob. 131ECh. 1.6 - Prob. 132ECh. 1.6 - Prob. 133ECh. 1.6 - Prob. 134ECh. 1.6 - Prob. 135ECh. 1.6 - Prob. 136ECh. 1.6 - Prob. 137ECh. 1.6 - Prob. 138ECh. 1.6 - Prob. 139ECh. 1.6 - Prob. 140ECh. 1.7 - Prob. 1ECh. 1.7 - Prob. 2ECh. 1.7 - Prob. 3ECh. 1.7 - Prob. 4ECh. 1.7 - Prob. 5ECh. 1.7 - Prob. 6ECh. 1.7 - Prob. 7ECh. 1.7 - Prob. 8ECh. 1.7 - Prob. 9ECh. 1.7 - Prob. 10ECh. 1.7 - Prob. 11ECh. 1.7 - Prob. 12ECh. 1.7 - Prob. 13ECh. 1.7 - Prob. 14ECh. 1.7 - Prob. 15ECh. 1.7 - Prob. 16ECh. 1.7 - Prob. 17ECh. 1.7 - Prob. 18ECh. 1.7 - Prob. 19ECh. 1.7 - Prob. 20ECh. 1.7 - Prob. 21ECh. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.7 - Prob. 24ECh. 1.7 - Prob. 25ECh. 1.7 - Prob. 26ECh. 1.7 - Prob. 27ECh. 1.7 - Prob. 28ECh. 1.7 - Prob. 29ECh. 1.7 - Prob. 30ECh. 1.7 - Prob. 31ECh. 1.7 - Prob. 32ECh. 1.7 - Prob. 33ECh. 1.7 - Prob. 34ECh. 1.7 - Prob. 35ECh. 1.7 - Prob. 36ECh. 1.7 - Prob. 37ECh. 1.7 - Prob. 38ECh. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Prob. 47RECh. 1 - Prob. 48RECh. 1 - Prob. 49RECh. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Prob. 52RECh. 1 - Prob. 53RECh. 1 - Prob. 54RECh. 1 - Prob. 55RECh. 1 - Prob. 56RECh. 1 - Prob. 57RECh. 1 - Prob. 58RECh. 1 - Prob. 59RECh. 1 - Prob. 60RECh. 1 - Prob. 61RECh. 1 - Prob. 62RECh. 1 - Prob. 63RECh. 1 - Prob. 64RECh. 1 - Prob. 65RECh. 1 - Prob. 66RECh. 1 - Prob. 67RECh. 1 - Prob. 68RECh. 1 - Prob. 69RECh. 1 - Prob. 70RECh. 1 - Prob. 71RECh. 1 - Prob. 72RECh. 1 - Prob. 73RECh. 1 - Prob. 74RECh. 1 - Prob. 75RECh. 1 - Prob. 76RECh. 1 - Prob. 77RECh. 1 - Prob. 78RECh. 1 - Prob. 79RECh. 1 - Prob. 80RECh. 1 - Prob. 81RECh. 1 - Prob. 82RECh. 1 - Prob. 83RECh. 1 - Prob. 84RECh. 1 - Prob. 85RECh. 1 - Prob. 86RECh. 1 - Prob. 87RECh. 1 - Prob. 88RECh. 1 - Prob. 89RECh. 1 - Prob. 90RECh. 1 - Prob. 91RECh. 1 - Prob. 92RECh. 1 - Prob. 93RECh. 1 - Prob. 94RECh. 1 - Prob. 95RECh. 1 - Prob. 96RECh. 1 - Prob. 97RECh. 1 - Prob. 98RECh. 1 - Prob. 99RECh. 1 - Prob. 100RECh. 1 - Prob. 101RECh. 1 - Prob. 102RECh. 1 - Prob. 103RECh. 1 - Prob. 104RECh. 1 - Prob. 105RECh. 1 - Prob. 106RECh. 1 - Prob. 107RECh. 1 - Prob. 108RECh. 1 - Prob. 109RECh. 1 - Prob. 110RECh. 1 - Prob. 111RECh. 1 - Prob. 112RECh. 1 - Prob. 113RECh. 1 - Prob. 114RECh. 1 - Prob. 115RECh. 1 - Prob. 116RECh. 1 - Prob. 117RECh. 1 - Prob. 118RECh. 1 - Prob. 119RECh. 1 - Prob. 120RECh. 1 - Prob. 121RECh. 1 - Prob. 122RECh. 1 - Prob. 123RECh. 1 - Prob. 124RECh. 1 - Prob. 125RECh. 1 - Prob. 126RECh. 1 - Prob. 127RECh. 1 - Prob. 128RECh. 1 - Prob. 129RECh. 1 - Prob. 130RECh. 1 - Prob. 131RECh. 1 - Prob. 132RECh. 1 - Prob. 133RECh. 1 - Prob. 134RECh. 1 - Prob. 135RECh. 1 - Prob. 136RECh. 1 - Prob. 137RECh. 1 - Prob. 138RECh. 1 - Prob. 139RECh. 1 - Prob. 140RECh. 1 - Prob. 141RECh. 1 - Prob. 142RECh. 1 - Prob. 143RECh. 1 - Prob. 144RECh. 1 - Prob. 145RECh. 1 - Prob. 146RECh. 1 - Prob. 147RECh. 1 - Prob. 148RECh. 1 - Prob. 149RECh. 1 - Prob. 150RECh. 1 - Prob. 151RECh. 1 - Prob. 1CTCh. 1 - Prob. 2CTCh. 1 - Prob. 3CTCh. 1 - Prob. 4CTCh. 1 - Prob. 5CTCh. 1 - Prob. 6CTCh. 1 - Prob. 7CTCh. 1 - Prob. 8CTCh. 1 - Prob. 9CTCh. 1 - Prob. 10CTCh. 1 - Prob. 11CTCh. 1 - Prob. 12CTCh. 1 - Prob. 13CTCh. 1 - Prob. 14CTCh. 1 - Prob. 15CTCh. 1 - Prob. 16CTCh. 1 - Prob. 17CTCh. 1 - Prob. 18CTCh. 1 - Prob. 19CTCh. 1 - Prob. 20CT
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