Chapter 2: Q.40 (page 90)

Determine algebraically whether each function is even, odd, or neither.
$f (x) = \sqrt[3]{2 x^{2} + 1}$

Short Answer

Expert verified

$f (x)$ is an even function.

Step by step solution

Given information.

The function, $f (x) = \sqrt[3]{2 x^{2} + 1}$ .

Write definition of even function and odd function.

A function $f (x)$ is said to be an even function if $f (- x) = f (x)$ .
A function $f (x)$ is said to be an odd function if $f (- x) = - f (x)$ .

Calculate f-x.

Replace $x$ by $- x$ into the function $f (x) = \sqrt[3]{2 x^{2} + 1}$ .

width="147">f-x=2-x2+13=2x2+13=fx

Clearly, $f (- x) = f (x)$

So by definition, $f (x)$ is an even function.

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Determine algebraically whether each function is even, odd, or neither.
$f (x) = \sqrt[3]{2 x^{2} + 1}$

Short Answer

Step by step solution

Given information.

Write definition of even function and odd function.

Calculate f-x.

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Determine algebraically whether each function is even, odd, or neither.fx=2x2+13

Short Answer

Step by step solution

Given information.

Write definition of even function and odd function.

Calculate f-x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Geometry

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Determine algebraically whether each function is even, odd, or neither.
$f (x) = \sqrt[3]{2 x^{2} + 1}$