/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 Determine whether each function ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 27

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

Short Answer

Expert verified
The function \(f(x) = x\sqrt{1-x^2}\) is odd.

Step by step solution

01

Substitute \(x\) for \(-x\)

Replace all occurences of \(x\) in the original function with \(-x\). This gives: \(f(-x) = -x\sqrt{1-(-x)^2} = -x\sqrt{1-x^2}\)
02

Compare \(f(-x)\) with \(f(x)\) and \(-f(x)\)

We now have to analyse our function \(f(-x) = -x\sqrt{1-x^2}\). Clearly, this is not equal to \(f(x) = x\sqrt{1-x^2}\) so the function is not even. However, multiply \(f(x)\) by -1 to get \(-f(x) = -x\sqrt{1-x^2}\), which is now identical to \(f(-x)\) so the function is odd.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}-2 x+y^{2}-15=0 $$

a. Graph the functions \(f(x)=x^{n}\) for \(n=2,4,\) and 6 in a \([-2,2,1]\) by \([-1,3,1]\) viewing rectangle. b. Graph the functions \(f(x)=x^{n}\) for \(n=1,3,\) and 5 in a \([-2,2,1]\) by \([-2,2,1]\) viewing rectangle. c. If \(n\) is positive and even, where is the graph of \(f(x)=x^{n}\) increasing and where is it decreasing? d. If \(n\) is positive and odd, what can you conclude about the graph of \(f(x)=x^{n}\) in terms of increasing or decreasing behavior? e. Graph all six functions in a \([-1,3,1]\) by \([-1,3,1]\) viewing rectangle. What do you observe about the graphs in terms of how flat or how steep they are?

Furry Finances A pet insurance policy has a monthly rate that is a function of the age of the insured dog or cat. For pets whose age does not exceed \(4,\) the monthly cost is \(\$ 20\). The cost then increases by \(\$ 2\) for each successive year of the pet's age. $$ \begin{array}{cc} \text { Age Not Exceeding } & \text { Monthly Cost } \\ \hline 4 & \$ 20 \\ 5 & \$ 22 \\ 6 & \$ 24 \end{array} $$ The cost schedule continues in this manner for ages not exceeding \(10 .\) The cost for pets whose ages exceed 10 is S40. Use this information to create a graph that shows the monthly cost of the insurance, \(f(x)\), for a pet of age \(x,\) where the function's domain is \([0,14]\)

Does \((x-3)^{2}+(y-5)^{2}=0\) represent the equation of a circle? If not, describe the graph of this equation.

determine whether each statement makes sense or does not make sense, and explain your reasoning. The graph of \((x-4)+(y+6)=25\) is a circle with radius 5 centered at \((4,-6)\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.