# the given function 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, Problem 65RE

a.

To determine

## To determine the given function is even, odd or neither.

Expert Solution

The given function f is neither even nor odd.

### Explanation of Solution

Given: The given function is f(x)=2x53x2+2

Calculation:

The given function is f(x)=2x53x2+2

f(x)=2(x)53(x)2+2=2x53x2+2since f(x)f(x)and f(x)f(x)

Hence, the given function f is neither even nor odd.

b.

To determine

### To determine the given function is even, odd or neither.

Expert Solution

The given function f is an odd function.

### Explanation of Solution

Given: The given function f(x)=x3x7

Calculation:

The given function f(x)=x3x7

f(x)=(x)3(x)7=x3+x7=(x3+x7)=f(x)

Therefore, f is an odd function.

c.

To determine

### To determine the given function is even, odd or neither.

Expert Solution

The given function f is an even function.

### Explanation of Solution

Given:

The given function f(x)=1x21+x2

Calculation: Let f(x)=1x21+x2

f(x)=1(x)21+(x)2          =1x21+x2          =f(x)

Hence, the given function f is an even function.

d.

To determine

### To determine the given function is even, odd or neither.

Expert Solution

The given function f is neither even nor odd.

### Explanation of Solution

Given: The given function

f(x)=1x+2

Calculation: The given function f(x)=1x+2

since f(x)f(x) and f(x)f(x)

we conclude that f is neither even nor odd.

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