Chapter 2: Q 42. (page 90)

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.
$h (x) = \frac{x}{x^{2} - 1}$

Short Answer

Expert verified

The given function $h (x) = \frac{x}{x^{2} - 1}$ is odd.

Step by step solution

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

The given function is: $h (x) = \frac{x}{x^{2} - 1}$

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,

$h (- x) = \frac{- x}{{(- x)}^{2} - 1} = \frac{- x}{x^{2} - 1} = - \frac{x}{x^{2} - 1}$

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

Step 3. Determine if the function is odd.

Find the function $- h (x)$ ,

$- h (x) = - \frac{x}{x^{2} - 1}$

Since role="math" localid="1645807726141" $h (- x) = - h (x), h$ is an odd function.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.
$h (x) = \frac{x}{x^{2} - 1}$

Short Answer

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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Discrete Mathematics

Calculus

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.h(x)=xx2-1

Short Answer

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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Discrete Mathematics

Calculus

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.
$h (x) = \frac{x}{x^{2} - 1}$