# Whether the function f ( x ) = x 4 − 16 is one-to-one.

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 10E
To determine

Expert Solution

## Answer to Problem 10E

The function f(x)=x416 is not a one-to one function.

### Explanation of Solution

Use horizontal line test to determine whether the function f(x)=x416 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 f(x)=x416 and perform the horizontal line test as shown below in Figure 1.

From Figure 1, it is observed that the horizontal line intersects the curve at two distinct points which means it fails the horizontal line test. Therefore, the function f(x)=x416 is not a one-to-one function.

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