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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.6, Problem 18E

(a)

To determine

**To explain:** Why the given graph *f* is one-to-one.

Expert Solution

Perform the horizontal line test for the given graph.

Draw a horizontal line such that it passes through the curve as shown in Figure 1.

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 is an one-to-one function.

(b)

To determine

**To find:** The domain and range of

Expert Solution

The domain of

The range of

Notice that the domain of the graph *f* is [−3, 3] and the range of the graph *f* is [−1, 3].

According to the definition of an inverse function, the domain of
*f* and the range of
*f*.

Thus, the domain of

(c)

To determine

**To find:** The value of

Expert Solution

The value of

From part (a) it is known that the function is one-to-one.

It is identified from the graph that

According to the definition of an inverse function,
*f* is one-to-one.

The value of

Thus, it can be concluded that the value of

(d)

To determine

**To estimate:** The value of

Expert Solution

The value of

From part (a) it is known that the function is one-to-one.

It is identified from the graph that

According to the definition of an inverse function,
*f* is one-to-one.

The value of

Thus, it can be estimated that the value of