BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.6, Problem 12E
To determine

Whether the function g(x)=x3 is one-to-one.

Expert Solution

Answer to Problem 12E

The function g(x)=x3 is one-to one.

Explanation of Solution

Express the given function as g(x)=x13 .

Use horizontal line test to determine whether the function g(x)=x13 is one-to-one.

Horizontal line test states that the graph of the function is one-to-one function if and only if a horizontal line intersects the graph exactly once.

Sketch the graph of the function g(x)=x13 and perform the horizontal line test as shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 12E

From Figure 1, it is observed that the horizontal line intersects the curve exactly at once which means it passes the horizontal line test. Therefore, the function g(x)=x3 is one-to-one.

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