Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.
$h (x) = \frac{- x^{3}}{3 x^{2} - 9}$

The given function $h (x) = \frac{- x^{3}}{3 x^{2} - 9}$ is an odd function.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write the given information and use the definition of odd and even function.

The given function is:

$h (x) = \frac{- x^{3}}{3 x^{2} - 9}$

A function $f$ is even if, for every number $x$ in its domain, the number $- x$ is also in the domain and $f (- x) = f (x)$ .

A function $f$ is odd if, for every number $x$ in its domain, the number $- x$ is also in the domain and $f (- x) = - f (x)$ .

Step 2. Determine if the function is even.

Replace $x$ by $- x$ in the given function,

$h (- x) = \frac{- {(- x)}^{3}}{3 {(- x)}^{2} - 9} = \frac{- {(- x)}^{3}}{3 {(x)}^{2} - 9} = \frac{x^{3}}{3 x^{2} - 9}$

Since $h (- x) \neq h (x), h$ is not an even function.

Step 3. Determine if the function is odd.

Find the function $- h (x)$ ,

role="math" localid="1645811470834" $- h (x) = - (\frac{- x^{3}}{3 x^{2} - 9}) = \frac{x^{3}}{3 x^{2} - 9}$

Since $h (- x) = - h (x), h$ is an odd function.

Find Study Materials for

Create Study Materials

Select your language

Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.
$h (x) = \frac{- x^{3}}{3 x^{2} - 9}$

Step by Step Solution

Step 1. Write the given information and use the definition of odd and even function.

Step 2. Determine if the function is even.

Step 3. Determine if the function is odd.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.h(x)=-x33x2-9

Step by Step Solution

Step 1. Write the given information and use the definition of odd and even function.

Step 2. Determine if the function is even.

Step 3. Determine if the function is odd.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.
$h (x) = \frac{- x^{3}}{3 x^{2} - 9}$