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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Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
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Chapter 10.3, Problem 16WE
To determine

Sketch the graph of the function g(x)=2x3 and with the help of horizontal-line test determine whether the function has an inverse function. If not say so.

Expert Solution & Answer
Check Mark

Answer to Problem 16WE

The graph of the function g(x)=2x3 has the inverse function g−1(x)=x32 .

Explanation of Solution

Given information: The given function is,

  g(x)=2x3 ....(1)

Formula used: The horizontal-line test for the graph of a function to have its inverse function, the graph must passes through the horizontal line test. It means if any line drawn horizontal parallel to (x) axis, cuts the graph at most one point then its inverse exists, else not.

Graph: The graph for the function is shown as,

  Algebra and Trigonometry: Structure and Method, Book 2, Chapter 10.3, Problem 16WE

Calculation: Since the given graph of function passes the horizontal line test. Therefore the graph of the function has the inverse function. Hence the inverse of the function g(x)=2x3 exist for the given graph and is evaluated as,

  y=2x3 ......(Plugging g(x)=y)(x)=2(y)3 ......(Exchanging variables)x3=2y ....(Cubed)y=x32......(Solving for variable (y))g−1(x)=x32......(Plugging y=g−1(x))

Hence, the inverse of function g(x)=(8x)3 is g−1(x)=x32 .

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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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