# Whether the function f ( x ) = 2 x 5 − 3 x 2 + 2 is odd, even or neither.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1, Problem 17RE

(a)

To determine

## Whether the function f(x)=2x5−3x2+2 is odd, even or neither.

Expert Solution

Solution:

The function f(x)=2x53x2+2 is neither an odd function nor an even function.

### Explanation of Solution

Definition used:

If f(x)=f(x), then the function f(x) is said to be an odd function.

If f(x)=f(x), then the function f(x) is said to be an even function.

Calculation:

Find the value of f(x) by substituting −x for x in f(x).

f(x)=2(x)53(x)2+2=2(x5)3x2+2=2x53x2+2

It is noticed that f(x) is neither in the form of f(x) nor in the form of f(x).

Therefore, the function f(x)=2x53x2+2 is neither an even function nor odd function.

(b)

To determine

### Whether the function f(x)=x3−x7 is odd, even or neither.

Expert Solution

Solution:

The function f(x)=x3x7 is an odd function.

### Explanation of Solution

Definition used:

If f(x)=f(x), then the function f(x) is said to be an odd function.

If f(x)=f(x), then the function f(x) is said to be an even function.

Calculation:

Find the value of f(x) by substituting −x for x in f(x).

f(x)=(x)3(x)7=x3+x7=(x3x7)=f(x)

Therefore, the function f(x)=x3x7 is an odd function.

(c)

To determine

### Whether the function f(x)=e−x2 is odd, even or neither.

Expert Solution

Solution:

The function f(x)=ex2 is an even function.

### Explanation of Solution

Definition used:

If f(x)=f(x), then the function f(x) is said to be an odd function.

If f(x)=f(x), then the function f(x) is said to be an even function.

Calculation:

Find the value of f(x) by substituting −x for x in f(x).

f(x)=e(x)2=ex2=f(x)

Therefore, the function f(x)=ex2 is an even function.

(d)

To determine

### Whether the function f(x)=1+sinx is odd, even or neither.

Expert Solution

Solution:

The function f(x)=1+sinx is neither an even function nor odd function.

### Explanation of Solution

Definition used:

If f(x)=f(x), then the function f(x) is said to be an odd function.

If f(x)=f(x), then the function f(x) is said to be an even function.

Calculation:

Find the value of f(x) by substituting −x for x in f(x).

f(x)=1+sin(x)=1sinx

It is noticed that f(x) is neither in the form of f(x) nor in the form of f(x).

Therefore, the function f(x)=1+sinx is neither an even function nor odd function.

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