Chapter 2: Q. 35 (page 90)

Determine algebraically whether each function is even, odd, or neither.
$g (x) = - 3 x^{2} - 5$

Short Answer

Expert verified

$g (x)$ is an even function.

Step by step solution

Given information.

The function: $g (x) = - 3 x^{2} - 5$

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 g-x.

Replace $x$ by $- x$ into the given function $g (x) = - 3 x^{2} - 5$ .

$g (- x) = - 3 {(- x)}^{2} - 5 = - 3 x^{2} - 5 = g (x)$

As, $g (- x) = g (x)$

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

Determine algebraically whether each function is even, odd, or neither.
$g (x) = - 3 x^{2} - 5$

Short Answer

Step by step solution

Given information.

Write definition of even function and odd function.

Calculate g-x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Determine algebraically whether each function is even, odd, or neither.gx=-3x2-5

Short Answer

Step by step solution

Given information.

Write definition of even function and odd function.

Calculate g-x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Determine algebraically whether each function is even, odd, or neither.
$g (x) = - 3 x^{2} - 5$