College Algebra Essentials
College Algebra Essentials
1st Edition
ISBN: 9780078035616
Author: Julie Miller
Publisher: MCG
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Textbook Question
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Chapter 4.1, Problem 45PE

a. Show that f(x) = 2 x – 3 defines a one-to-one function.

b. Write an equation for f 1 ( x ) .

c. Graph y = f ( x ) and y = f − 1 ( x ) on the same coordinate system.

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Chapter 4 Solutions

College Algebra Essentials

Ch. 4.1 - Skill Practice 1 Determine whether function f is a...Ch. 4.1 - Prob. 2SPCh. 4.1 - Prob. 3SPCh. 4.1 - Prob. 4SPCh. 4.1 - Prob. 5SPCh. 4.1 - Prob. 6SPCh. 4.1 - Prob. 7SPCh. 4.1 - Prob. 8SPCh. 4.1 - Prob. 1PECh. 4.1 - Prob. 2PE
Ch. 4.1 - Prob. 3PECh. 4.1 - Prob. 4PECh. 4.1 - Prob. 5PECh. 4.1 - Prob. 6PECh. 4.1 - Prob. 7PECh. 4.1 - Prob. 8PECh. 4.1 - Prob. 9PECh. 4.1 - Prob. 10PECh. 4.1 - Prob. 11PECh. 4.1 - Prob. 12PECh. 4.1 - Prob. 13PECh. 4.1 - Prob. 14PECh. 4.1 - Prob. 15PECh. 4.1 - Prob. 16PECh. 4.1 - Prob. 17PECh. 4.1 - Prob. 18PECh. 4.1 - Prob. 19PECh. 4.1 - Prob. 20PECh. 4.1 - Prob. 21PECh. 4.1 - Prob. 22PECh. 4.1 - Prob. 23PECh. 4.1 - Prob. 24PECh. 4.1 - Prob. 25PECh. 4.1 - Prob. 26PECh. 4.1 - Prob. 27PECh. 4.1 - Prob. 28PECh. 4.1 - Prob. 29PECh. 4.1 - Prob. 30PECh. 4.1 - Prob. 31PECh. 4.1 - Prob. 32PECh. 4.1 - Prob. 33PECh. 4.1 - Prob. 34PECh. 4.1 - Prob. 35PECh. 4.1 - Prob. 36PECh. 4.1 - Prob. 37PECh. 4.1 - Prob. 38PECh. 4.1 - Prob. 39PECh. 4.1 - Prob. 40PECh. 4.1 - Prob. 41PECh. 4.1 - Prob. 42PECh. 4.1 - Prob. 43PECh. 4.1 - The monthly sales for January for a whole foods...Ch. 4.1 - a. Show that f(x) = 2 x 3 defines a one-to-one...Ch. 4.1 - a. Show that f(x) = 4 x+ 4 defines a one-to-one...Ch. 4.1 - For Exercises 4758, a one-to-one function is...Ch. 4.1 - For Exercises 4758, a one-to-one function is...Ch. 4.1 - For Exercises 4758, a one-to-one function is...Ch. 4.1 - Prob. 50PECh. 4.1 - Prob. 51PECh. 4.1 - Prob. 52PECh. 4.1 - Prob. 53PECh. 4.1 - Prob. 54PECh. 4.1 - Prob. 55PECh. 4.1 - Prob. 56PECh. 4.1 - Prob. 57PECh. 4.1 - Prob. 58PECh. 4.1 - Prob. 59PECh. 4.1 - Prob. 60PECh. 4.1 - Prob. 61PECh. 4.1 - Prob. 62PECh. 4.1 - Prob. 63PECh. 4.1 - Prob. 64PECh. 4.1 - Prob. 65PECh. 4.1 - Prob. 66PECh. 4.1 - Prob. 67PECh. 4.1 - Prob. 68PECh. 4.1 - Prob. 69PECh. 4.1 - Prob. 70PECh. 4.1 - Prob. 71PECh. 4.1 - Prob. 72PECh. 4.1 - Prob. 73PECh. 4.1 - Prob. 74PECh. 4.1 - Prob. 75PECh. 4.1 - Prob. 76PECh. 4.1 - Prob. 77PECh. 4.1 - Prob. 78PECh. 4.1 - Prob. 79PECh. 4.1 - Prob. 80PECh. 4.1 - Prob. 81PECh. 4.1 - Prob. 82PECh. 4.1 - Prob. 83PECh. 4.1 - Prob. 84PECh. 4.1 - Prob. 85PECh. 4.1 - Prob. 86PECh. 4.1 - Prob. 87PECh. 4.1 - Prob. 88PECh. 4.1 - Prob. 89PECh. 4.1 - Prob. 90PECh. 4.1 - Prob. 91PECh. 4.1 - Prob. 92PECh. 4.1 - Prob. 93PECh. 4.1 - Prob. 94PECh. 4.1 - Prob. 95PECh. 4.1 - Prob. 96PECh. 4.1 - Prob. 97PECh. 4.1 - Prob. 98PECh. 4.1 - Show that every increasing function is one-to-one.Ch. 4.1 - Prob. 100PECh. 4.1 - Prob. 101PECh. 4.2 - Prob. 1SPCh. 4.2 - Prob. 2SPCh. 4.2 - Prob. 3SPCh. 4.2 - Prob. 4SPCh. 4.2 - Prob. 5SPCh. 4.2 - Prob. 1PECh. 4.2 - Prob. 2PECh. 4.2 - Prob. 3PECh. 4.2 - Prob. 4PECh. 4.2 - Prob. 5PECh. 4.2 - Prob. 6PECh. 4.2 - Prob. 7PECh. 4.2 - Prob. 8PECh. 4.2 - Prob. 9PECh. 4.2 - Prob. 10PECh. 4.2 - Prob. 11PECh. 4.2 - Prob. 12PECh. 4.2 - Prob. 13PECh. 4.2 - Prob. 14PECh. 4.2 - Prob. 15PECh. 4.2 - Prob. 16PECh. 4.2 - Prob. 17PECh. 4.2 - Prob. 18PECh. 4.2 - Prob. 19PECh. 4.2 - Prob. 20PECh. 4.2 - Prob. 21PECh. 4.2 - Prob. 22PECh. 4.2 - Prob. 23PECh. 4.2 - Prob. 24PECh. 4.2 - Prob. 25PECh. 4.2 - Prob. 26PECh. 4.2 - Prob. 27PECh. 4.2 - Prob. 28PECh. 4.2 - Prob. 29PECh. 4.2 - Prob. 30PECh. 4.2 - Prob. 31PECh. 4.2 - 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Prob. 120PECh. 4.3 - Prob. 121PECh. 4.3 - Prob. 122PECh. 4.3 - Prob. 123PECh. 4.3 - Prob. 124PECh. 4.3 - Prob. 125PECh. 4.3 - Prob. 126PECh. 4.3 - Prob. 127PECh. 4.3 - Prob. 128PECh. 4.3 - Prob. 129PECh. 4.3 - Prob. 130PECh. 4.4 - Prob. 1SPCh. 4.4 - Prob. 2SPCh. 4.4 - Prob. 3SPCh. 4.4 - Prob. 4SPCh. 4.4 - Prob. 5SPCh. 4.4 - Prob. 6SPCh. 4.4 - Prob. 7SPCh. 4.4 - Prob. 8SPCh. 4.4 - Prob. 1PECh. 4.4 - Prob. 2PECh. 4.4 - Prob. 3PECh. 4.4 - Prob. 4PECh. 4.4 - Prob. 5PECh. 4.4 - Prob. 6PECh. 4.4 - Prob. 7PECh. 4.4 - Prob. 8PECh. 4.4 - Prob. 9PECh. 4.4 - Prob. 10PECh. 4.4 - Prob. 11PECh. 4.4 - Prob. 12PECh. 4.4 - Prob. 13PECh. 4.4 - Prob. 14PECh. 4.4 - Prob. 15PECh. 4.4 - Prob. 16PECh. 4.4 - Prob. 17PECh. 4.4 - Prob. 18PECh. 4.4 - Prob. 19PECh. 4.4 - For Exercises 1722, use the product property of...Ch. 4.4 - Prob. 21PECh. 4.4 - Prob. 22PECh. 4.4 - Prob. 23PECh. 4.4 - Prob. 24PECh. 4.4 - Prob. 25PECh. 4.4 - Prob. 26PECh. 4.4 - Prob. 27PECh. 4.4 - Prob. 28PECh. 4.4 - Prob. 29PECh. 4.4 - Prob. 30PECh. 4.4 - Prob. 31PECh. 4.4 - Prob. 32PECh. 4.4 - Prob. 33PECh. 4.4 - Prob. 34PECh. 4.4 - Prob. 35PECh. 4.4 - Prob. 36PECh. 4.4 - Prob. 37PECh. 4.4 - Prob. 38PECh. 4.4 - Prob. 39PECh. 4.4 - Prob. 40PECh. 4.4 - Prob. 41PECh. 4.4 - Prob. 42PECh. 4.4 - Prob. 43PECh. 4.4 - Prob. 44PECh. 4.4 - Prob. 45PECh. 4.4 - Prob. 46PECh. 4.4 - Prob. 47PECh. 4.4 - Prob. 48PECh. 4.4 - Prob. 49PECh. 4.4 - Prob. 50PECh. 4.4 - Prob. 51PECh. 4.4 - Prob. 52PECh. 4.4 - Prob. 53PECh. 4.4 - Prob. 54PECh. 4.4 - Prob. 55PECh. 4.4 - Prob. 56PECh. 4.4 - Prob. 57PECh. 4.4 - Prob. 58PECh. 4.4 - Prob. 59PECh. 4.4 - Prob. 60PECh. 4.4 - Prob. 61PECh. 4.4 - Prob. 62PECh. 4.4 - Prob. 63PECh. 4.4 - Prob. 64PECh. 4.4 - Prob. 65PECh. 4.4 - Prob. 66PECh. 4.4 - Prob. 67PECh. 4.4 - Prob. 68PECh. 4.4 - Prob. 69PECh. 4.4 - Prob. 70PECh. 4.4 - Prob. 71PECh. 4.4 - Prob. 72PECh. 4.4 - Prob. 73PECh. 4.4 - Prob. 74PECh. 4.4 - Prob. 75PECh. 4.4 - Prob. 76PECh. 4.4 - Prob. 77PECh. 4.4 - Prob. 78PECh. 4.4 - Prob. 79PECh. 4.4 - Prob. 80PECh. 4.4 - 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Prob. 18PECh. 4.6 - Prob. 19PECh. 4.6 - Prob. 20PECh. 4.6 - Prob. 21PECh. 4.6 - Prob. 22PECh. 4.6 - Prob. 23PECh. 4.6 - Prob. 24PECh. 4.6 - Prob. 25PECh. 4.6 - Prob. 26PECh. 4.6 - Prob. 27PECh. 4.6 - Prob. 28PECh. 4.6 - Prob. 29PECh. 4.6 - Prob. 30PECh. 4.6 - Prob. 31PECh. 4.6 - Prob. 32PECh. 4.6 - Prob. 33PECh. 4.6 - Prob. 34PECh. 4.6 - Prob. 35PECh. 4.6 - Prob. 36PECh. 4.6 - Prob. 37PECh. 4.6 - Prob. 38PECh. 4.6 - Prob. 39PECh. 4.6 - The population of Canada P(t) (in millions) since...Ch. 4.6 - Prob. 41PECh. 4.6 - Prob. 42PECh. 4.6 - Prob. 43PECh. 4.6 - Prob. 44PECh. 4.6 - Prob. 45PECh. 4.6 - Prob. 46PECh. 4.6 - Prob. 47PECh. 4.6 - Prob. 48PECh. 4.6 - Prob. 49PECh. 4.6 - Prob. 50PECh. 4.6 - Prob. 51PECh. 4.6 - Prob. 52PECh. 4.6 - Prob. 53PECh. 4.6 - Prob. 54PECh. 4.6 - Prob. 55PECh. 4.6 - Prob. 56PECh. 4.6 - Prob. 57PECh. 4.6 - The sales of a book tend to increase over the...Ch. 4.6 - Prob. 59PECh. 4.6 - Prob. 60PECh. 4.6 - Prob. 61PECh. 4.6 - Prob. 62PECh. 4.6 - Prob. 63PECh. 4.6 - Prob. 64PECh. 4.6 - Prob. 65PECh. 4.6 - Prob. 66PECh. 4.6 - Prob. 67PECh. 4 - Prob. 1PRECh. 4 - Prob. 2PRECh. 4 - Prob. 3PRECh. 4 - Prob. 4PRECh. 4 - Prob. 5PRECh. 4 - Prob. 6PRECh. 4 - Prob. 7PRECh. 4 - Prob. 8PRECh. 4 - Prob. 9PRECh. 4 - Prob. 10PRECh. 4 - Prob. 11PRECh. 4 - Prob. 12PRECh. 4 - Prob. 13PRECh. 4 - Prob. 14PRECh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - For Exercises 1819, use the formulas on page 450....Ch. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - Prob. 91RECh. 4 - Prob. 92RECh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - Prob. 10TCh. 4 - Prob. 11TCh. 4 - Prob. 12TCh. 4 - Prob. 13TCh. 4 - Prob. 14TCh. 4 - Prob. 15TCh. 4 - Prob. 16TCh. 4 - Prob. 17TCh. 4 - Prob. 18TCh. 4 - Prob. 19TCh. 4 - Prob. 20TCh. 4 - Prob. 21TCh. 4 - Prob. 22TCh. 4 - Prob. 23TCh. 4 - Prob. 24TCh. 4 - Prob. 25TCh. 4 - Prob. 26TCh. 4 - Prob. 27TCh. 4 - Prob. 28TCh. 4 - Prob. 29TCh. 4 - Prob. 30TCh. 4 - Prob. 31TCh. 4 - Prob. 32TCh. 4 - Prob. 33TCh. 4 - Prob. 34TCh. 4 - Prob. 35TCh. 4 - Prob. 36TCh. 4 - Prob. 37TCh. 4 - Prob. 38TCh. 4 - Prob. 39TCh. 4 - Prob. 40TCh. 4 - Prob. 41TCh. 4 - Prob. 42TCh. 4 - Prob. 1CRECh. 4 - Prob. 2CRECh. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRECh. 4 - Prob. 6CRECh. 4 - Prob. 7CRECh. 4 - Prob. 8CRECh. 4 - Prob. 9CRECh. 4 - Prob. 10CRECh. 4 - Prob. 11CRECh. 4 - Prob. 12CRECh. 4 - Prob. 13CRECh. 4 - Prob. 14CRECh. 4 - Prob. 15CRECh. 4 - Prob. 16CRECh. 4 - Prob. 17CRECh. 4 - Prob. 18CRECh. 4 - Write the expression as a single logarithm and...Ch. 4 - Prob. 20CRE
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