# To state : whether the function f ( x ) = x 3 − x 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 79E
To determine

## To state : whether the function f(x)=x3−x is even, odd or neither.

Expert Solution

The function f(x)=x3x is odd.

### Explanation of Solution

Given information :

The function is f(x)=x3x

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)=x3xf(x)=(x)3(x)f(x)=x3+xf(x)=(x3x)f(x)=f(x)

Therefore, function f(x)=x3x is odd function.

Hence, the graph of f(x)=x3x is symmetric about x -axis, ### Have a homework question?

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