Chapter 2: Q 43. (page 90)

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

Short Answer

Expert verified

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

Step by step solution

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

The given function is:

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

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.

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

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.

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

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

Applied Mathematics

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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