# To state : whether the function f ( x ) = x 4 − 4 x 2 is even, odd or neither.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.5, Problem 78E
To determine

## To state : whether the function f(x)=x4−4x2 is even, odd or neither.

Expert Solution

The function f(x)=x44x2 is even.

### Explanation of Solution

Given information :

The function is f(x)=x44x2

The function f is even if f(x)=f(x) for all x in the domain of f .

The function f is odd if f(x)=f(x) for all x in the domain of f .

f(x)=x44x2f(x)=(x)44(x)2f(x)=x44x2 f(x)=f(x)

Therefore, the function f(x)=x44x2 is even function.

Hence, the graph of the function f(x)=x44x2 is symmetric about the y -axis.

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