Explanation Given: The function, g ( x ) = 0.5 x 3 − 2 One-to-one functions are those functions for which every element of the range of the function corresponds to exactly one element of the domain. If a horizontal line intersects a function's graph more than once, then the function is not one-to-one. The graph of the given function can be drawn using a graphing calculator and then subject it to the horizontal line test in the given domain [-10, 10]. If a function is determined to be One-to-one, then we can say that its inverse exists. To find the inverse function the following steps may be carried out. First, replace f ( x ) with y . Replace every x with a y and replace every y with an x . Solve the equation for y . Replace y with f − 1 ( x ) . Calculations: Description g ( x ) = 0.5 x 3 − 2 Step 1: Use the graphing calculator to plot the function y 1 = 0.5 x 3 − 2 and a horizontal line y 2 = 1 for reference P l o t 1 P l o t 2 P l o t 3 \ Y 1 = 0.5 x 3 − 2 \ Y 2 = 1 \ Y 3 = \ Y 4 = \ Y 5 = The horizontal line intersects the given function never more than once. Therefore, the given function is one-to-one in the given interval. Step 2: To find the inverse of the given function, follow the steps. First, replace g ( x ) with y . g ( x ) = 0.5 x 3 − 2 y = 0.5 x 3 − 2 Step 3: Replace every x with a y and replace every y with an x . ⇒ x = 0.5 y 3 − 2 Step 4: Solve the equation for y

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ISBN: 9781264241590

Author: Miller

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Chapter 8.2, Problem 73PE

To determine

Graph of the given function using a graphing calculator

Whether the given function is one-to-one in the given interval

The inverse of the given function and graph the same

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Chapter 8.2, Problem 72PE

Chapter 8.2, Problem 74PE

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Chapter 8 Solutions

INTERMEDIATE ALGEBRA - ALEKS 360 ACCESS

Ch. 8.1 - a. Given the functions f and g, the function...Ch. 8.1 - Given fx=x2 and gx=2x3, find a. f2 b. g2 c. f+g2 Ch. 8.1 - Prob. 3PE Ch. 8.1 - For Exercise 3-14, refer to the function defined...Ch. 8.1 - For Exercise 3-14, refer to the function defined...Ch. 8.1 - Prob. 6PE Ch. 8.1 - Prob. 7PE Ch. 8.1 - Prob. 8PE Ch. 8.1 - For Exercise 3-14, refer to the function defined...Ch. 8.1 - Prob. 10PE

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Graph of the given function using a graphing calculator Whether the given function is one-to-one in the given interval The inverse of the given function and graph the same