Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Concept explainers

Domain
In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.
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Chapter 10.4, Problem 35WE
To determine

Sketch the graph of the function f(x)=6x and its inverse on the same pair of coordinate axis. Also label three points on each graph.

Expert Solution & Answer
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Explanation of Solution

Given information: The given function is,

  f(x)=6x

Concept used: In order to find the inverse of a given function f(x) write f(x)=y and exchange the variables (x) and (y) and solve for the variable (y) . At last write y=f−1(x) which is the required inverse of the function f(x) .

Calculation: For the given function f(x)=6x the inverse is evaluated as,

  y=6x......(Plugging f(x)=y)(x)=6(y)......(Exchanging variables)ln(x)=(y)ln(6)....(Take log both side)y=ln6(x)......(Solving for variable (y))f−1(x)=ln6(x)......(Plugging y=f−1(x))

Hence, the inverse of function f(x)=6x is f−1(x)=ln6(x) .

Graph: Now the graph for the function and its inverse is shown as,

  Algebra and Trigonometry: Structure and Method, Book 2, Chapter 10.4, Problem 35WE

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Chapter 10 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 10.1 - Prob. 1OECh. 10.1 - Prob. 2OECh. 10.1 - Prob. 3OECh. 10.1 - Prob. 4OECh. 10.1 - Prob. 5OECh. 10.1 - Prob. 6OECh. 10.1 - Prob. 7OECh. 10.1 - Prob. 8OECh. 10.1 - Prob. 9OECh. 10.1 - Prob. 10OE
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Prob. 37WECh. 10.6 - Prob. 38WECh. 10.6 - Prob. 39WECh. 10.6 - Prob. 40WECh. 10.6 - Prob. 41WECh. 10.6 - Prob. 42WECh. 10.7 - Prob. 1OECh. 10.7 - Prob. 2OECh. 10.7 - Prob. 3OECh. 10.7 - Prob. 4OECh. 10.7 - Prob. 1PCh. 10.7 - Prob. 2PCh. 10.7 - Prob. 3PCh. 10.7 - Prob. 4PCh. 10.7 - Prob. 5PCh. 10.7 - Prob. 6PCh. 10.7 - Prob. 7PCh. 10.7 - Prob. 8PCh. 10.7 - Prob. 9PCh. 10.7 - Prob. 10PCh. 10.7 - Prob. 11PCh. 10.7 - Prob. 12PCh. 10.7 - Prob. 13PCh. 10.7 - Prob. 14PCh. 10.7 - Prob. 15PCh. 10.7 - Prob. 16PCh. 10.7 - Prob. 17PCh. 10.7 - Prob. 18PCh. 10.7 - Prob. 19PCh. 10.7 - Prob. 20PCh. 10.7 - Prob. 21PCh. 10.7 - Prob. 22PCh. 10.7 - Prob. 1MRECh. 10.7 - Prob. 2MRECh. 10.7 - Prob. 3MRECh. 10.7 - Prob. 4MRECh. 10.7 - Prob. 5MRECh. 10.7 - Prob. 6MRECh. 10.7 - Prob. 7MRECh. 10.7 - Prob. 8MRECh. 10.7 - Prob. 9MRECh. 10.7 - Prob. 10MRECh. 10.7 - Prob. 11MRECh. 10.7 - Prob. 12MRECh. 10.8 - Prob. 1OECh. 10.8 - Prob. 2OECh. 10.8 - Prob. 3OECh. 10.8 - Prob. 4OECh. 10.8 - Prob. 5OECh. 10.8 - Prob. 6OECh. 10.8 - 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