# To prove : the function f ( x ) = x n is even or odd

### 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 93E
To determine

## To prove : the function f(x)=xn is even or odd

Expert Solution

### Explanation of Solution

Given information : the function is f(x)=xn

Proof : A function is even if and only if

f(x)=f(x),xDf

A function is odd if and only if

f(x)=f(x),xDf

For even exponents 2,4,6,...... the function f is even, because opposite values of the variable x produce the same values for the function f

(x)2=x2,(x)4=x4,(x)6=x6f(x)=f(x)

For odd exponents 1,3,5,...... the function f is odd, because opposite values of the variable x produce the same values for the function f

(x)1=x1,(x)3=x3,(x)5=x5f(x)=f(x)

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