Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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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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Question
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Chapter 3.4, Problem 43E

(a)

To determine

To give:An example of function that is its own inverse.

(a)

Expert Solution
Check Mark

Answer to Problem 43E

An example of function that is its own inverse is y=x .

Explanation of Solution

Consider the function.

  y=x

Its inverse is,

  y−1=x

Therefore, an example of function that is its own inverse is y=x .

(b)

To determine

The symmetry that both the graph should exihibit.

(b)

Expert Solution
Check Mark

Answer to Problem 43E

The graph of both the function should be symmetric about the origin.

Explanation of Solution

Consider the function.

  y=x

Its inverse is,

  y−1=x

The graph of both the function should be symmetric about the origin.

(c)

To determine

To find: Whether all the function with such type of symmetry be their own inverse.

(c)

Expert Solution
Check Mark

Answer to Problem 43E

No, all the function with such type of symmetry are not their own inverse always.

Explanation of Solution

Consider the function.

  y=x3

Its inverse is,

  y−1=x3

So, the function and inverse are not same.

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Chapter 3.4, Problem 42E
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Chapter 3.4, Problem 44E

Chapter 3 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 3.1 - Prob. 1CFUCh. 3.1 - Prob. 2CFUCh. 3.1 - Prob. 3CFUCh. 3.1 - Prob. 4CFUCh. 3.1 - Prob. 5CFUCh. 3.1 - Prob. 6CFUCh. 3.1 - Prob. 7CFUCh. 3.1 - Prob. 8CFUCh. 3.1 - Prob. 9CFUCh. 3.1 - Prob. 10CFU
Ch. 3.1 - Prob. 11CFUCh. 3.1 - Prob. 12CFUCh. 3.1 - Prob. 13CFUCh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.2 - Prob. 1CFUCh. 3.2 - Prob. 2CFUCh. 3.2 - Prob. 3CFUCh. 3.2 - Prob. 4CFUCh. 3.2 - Prob. 5CFUCh. 3.2 - Prob. 6CFUCh. 3.2 - Prob. 7CFUCh. 3.2 - Prob. 8CFUCh. 3.2 - Prob. 9CFUCh. 3.2 - Prob. 10CFUCh. 3.2 - Prob. 11CFUCh. 3.2 - Prob. 12CFUCh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.3 - Prob. 1CFUCh. 3.3 - Prob. 2CFUCh. 3.3 - Prob. 3CFUCh. 3.3 - Prob. 4CFUCh. 3.3 - Prob. 5CFUCh. 3.3 - Prob. 6CFUCh. 3.3 - Prob. 7CFUCh. 3.3 - Prob. 8CFUCh. 3.3 - Prob. 9CFUCh. 3.3 - Prob. 10CFUCh. 3.3 - Prob. 11CFUCh. 3.3 - Prob. 12CFUCh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 1MCQCh. 3.3 - Prob. 2MCQCh. 3.3 - Prob. 3MCQCh. 3.3 - Prob. 4MCQCh. 3.3 - Prob. 5MCQCh. 3.3 - Prob. 6MCQCh. 3.3 - Prob. 7MCQCh. 3.3 - Prob. 8MCQCh. 3.3 - Prob. 9MCQCh. 3.3 - Prob. 10MCQCh. 3.4 - Prob. 1CFUCh. 3.4 - Prob. 2CFUCh. 3.4 - Prob. 3CFUCh. 3.4 - Prob. 4CFUCh. 3.4 - Prob. 5CFUCh. 3.4 - Prob. 6CFUCh. 3.4 - Prob. 7CFUCh. 3.4 - Prob. 8CFUCh. 3.4 - Prob. 9CFUCh. 3.4 - Prob. 10CFUCh. 3.4 - Prob. 11CFUCh. 3.4 - Prob. 12CFUCh. 3.4 - Prob. 13CFUCh. 3.4 - Prob. 14CFUCh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Prob. 53ECh. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.5 - Prob. 1CFUCh. 3.5 - Prob. 2CFUCh. 3.5 - Prob. 3CFUCh. 3.5 - Prob. 4CFUCh. 3.5 - Prob. 5CFUCh. 3.5 - Prob. 6CFUCh. 3.5 - Prob. 7CFUCh. 3.5 - Prob. 8CFUCh. 3.5 - Prob. 9CFUCh. 3.5 - Prob. 10CFUCh. 3.5 - Prob. 11CFUCh. 3.5 - Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - Prob. 37ECh. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - Prob. 41ECh. 3.5 - Prob. 42ECh. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - Prob. 45ECh. 3.5 - Prob. 46ECh. 3.5B - Prob. 1GCECh. 3.5B - Prob. 2GCECh. 3.5B - Prob. 3GCECh. 3.5B - Prob. 4GCECh. 3.5B - Prob. 5GCECh. 3.5B - Prob. 6GCECh. 3.5B - Prob. 7GCECh. 3.5B - Prob. 8GCECh. 3.5B - Prob. 9GCECh. 3.5B - Prob. 10GCECh. 3.5B - Prob. 11GCECh. 3.5B - Prob. 12GCECh. 3.5B - Prob. 13GCECh. 3.5B - Prob. 14GCECh. 3.6 - Prob. 1CFUCh. 3.6 - Prob. 2CFUCh. 3.6 - Prob. 3CFUCh. 3.6 - Prob. 4CFUCh. 3.6 - Prob. 5CFUCh. 3.6 - Prob. 6CFUCh. 3.6 - Prob. 7CFUCh. 3.6 - Prob. 8CFUCh. 3.6 - Prob. 9CFUCh. 3.6 - Prob. 10CFUCh. 3.6 - Prob. 11CFUCh. 3.6 - Prob. 12CFUCh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.7 - Prob. 1CFUCh. 3.7 - Prob. 2CFUCh. 3.7 - Prob. 3CFUCh. 3.7 - Prob. 4CFUCh. 3.7 - Prob. 5CFUCh. 3.7 - Prob. 6CFUCh. 3.7 - Prob. 7CFUCh. 3.7 - Prob. 8CFUCh. 3.7 - Prob. 9CFUCh. 3.7 - Prob. 10CFUCh. 3.7 - Prob. 11CFUCh. 3.7 - Prob. 12CFUCh. 3.7 - Prob. 13CFUCh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - Prob. 17ECh. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Prob. 20ECh. 3.7 - Prob. 21ECh. 3.7 - Prob. 22ECh. 3.7 - Prob. 23ECh. 3.7 - Prob. 24ECh. 3.7 - Prob. 25ECh. 3.7 - Prob. 26ECh. 3.7 - Prob. 27ECh. 3.7 - Prob. 28ECh. 3.7 - Prob. 29ECh. 3.7 - Prob. 30ECh. 3.7 - Prob. 31ECh. 3.7 - Prob. 32ECh. 3.7 - Prob. 33ECh. 3.7 - Prob. 34ECh. 3.7 - Prob. 35ECh. 3.7 - Prob. 36ECh. 3.7 - Prob. 37ECh. 3.7 - Prob. 38ECh. 3.7 - Prob. 39ECh. 3.7 - Prob. 40ECh. 3.7 - Prob. 41ECh. 3.7 - Prob. 42ECh. 3.7 - Prob. 43ECh. 3.7 - Prob. 44ECh. 3.7 - Prob. 45ECh. 3.7 - Prob. 46ECh. 3.7 - Prob. 47ECh. 3.7 - Prob. 48ECh. 3.7 - Prob. 49ECh. 3.7 - Prob. 50ECh. 3.7 - Prob. 51ECh. 3.7 - Prob. 52ECh. 3.7 - Prob. 53ECh. 3.7 - Prob. 54ECh. 3.7 - Prob. 55ECh. 3.7 - Prob. 56ECh. 3.8 - Prob. 1CFUCh. 3.8 - Prob. 2CFUCh. 3.8 - Prob. 3CFUCh. 3.8 - Prob. 4CFUCh. 3.8 - Prob. 5CFUCh. 3.8 - Prob. 6CFUCh. 3.8 - Prob. 7CFUCh. 3.8 - Prob. 8CFUCh. 3.8 - Prob. 9CFUCh. 3.8 - Prob. 10CFUCh. 3.8 - Prob. 11CFUCh. 3.8 - Prob. 12CFUCh. 3.8 - Prob. 13ECh. 3.8 - Prob. 14ECh. 3.8 - Prob. 15ECh. 3.8 - Prob. 16ECh. 3.8 - Prob. 17ECh. 3.8 - Prob. 18ECh. 3.8 - Prob. 19ECh. 3.8 - Prob. 20ECh. 3.8 - Prob. 21ECh. 3.8 - Prob. 22ECh. 3.8 - Prob. 23ECh. 3.8 - Prob. 24ECh. 3.8 - Prob. 25ECh. 3.8 - Prob. 26ECh. 3.8 - Prob. 27ECh. 3.8 - Prob. 28ECh. 3.8 - Prob. 29ECh. 3.8 - Prob. 30ECh. 3.8 - Prob. 31ECh. 3.8 - Prob. 32ECh. 3.8 - Prob. 33ECh. 3.8 - Prob. 34ECh. 3.8 - Prob. 35ECh. 3.8 - Prob. 36ECh. 3.8 - Prob. 37ECh. 3.8 - Prob. 38ECh. 3.8 - Prob. 39ECh. 3 - Prob. 1SGACh. 3 - Prob. 2SGACh. 3 - Prob. 3SGACh. 3 - Prob. 4SGACh. 3 - Prob. 5SGACh. 3 - Prob. 6SGACh. 3 - Prob. 7SGACh. 3 - Prob. 8SGACh. 3 - Prob. 9SGACh. 3 - Prob. 10SGACh. 3 - Prob. 11SGACh. 3 - Prob. 12SGACh. 3 - Prob. 13SGACh. 3 - Prob. 14SGACh. 3 - Prob. 15SGACh. 3 - Prob. 16SGACh. 3 - Prob. 17SGACh. 3 - Prob. 18SGACh. 3 - Prob. 19SGACh. 3 - Prob. 20SGACh. 3 - Prob. 21SGACh. 3 - Prob. 22SGACh. 3 - Prob. 23SGACh. 3 - Prob. 24SGACh. 3 - Prob. 25SGACh. 3 - Prob. 26SGACh. 3 - Prob. 27SGACh. 3 - Prob. 28SGACh. 3 - Prob. 29SGACh. 3 - Prob. 30SGACh. 3 - Prob. 31SGACh. 3 - Prob. 32SGACh. 3 - Prob. 33SGACh. 3 - Prob. 34SGACh. 3 - Prob. 35SGACh. 3 - Prob. 36SGACh. 3 - Prob. 37SGACh. 3 - Prob. 38SGACh. 3 - Prob. 39SGACh. 3 - Prob. 40SGACh. 3 - Prob. 41SGACh. 3 - Prob. 42SGACh. 3 - Prob. 43SGACh. 3 - Prob. 44SGACh. 3 - Prob. 45SGACh. 3 - Prob. 46SGACh. 3 - Prob. 47SGACh. 3 - Prob. 48SGACh. 3 - Prob. 49SGACh. 3 - Prob. 50SGACh. 3 - Prob. 51SGACh. 3 - Prob. 52SGACh. 3 - Prob. 53SGACh. 3 - Prob. 54SGACh. 3 - Prob. 55SGACh. 3 - Prob. 56SGACh. 3 - Prob. 57SGACh. 3 - Prob. 58SGACh. 3 - Prob. 59SGACh. 3 - Prob. 60SGACh. 3 - Prob. 61SGACh. 3 - Prob. 1SAPCh. 3 - Prob. 2SAPCh. 3 - Prob. 3SAPCh. 3 - Prob. 4SAPCh. 3 - Prob. 5SAPCh. 3 - Prob. 6SAPCh. 3 - Prob. 7SAPCh. 3 - Prob. 8SAPCh. 3 - Prob. 9SAPCh. 3 - Prob. 10SAP

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