We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Introduction to Functions

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : Inverse Functions

What is the inverse of the following function?

$f(x)=-2+\sqrt{x-1}$

Possible Answers:

$f^{-1}(x)=x-1$

$f^{-1}(x)=x^{2}+4x+5$

There is no inverse for this function.

$f^{-1}(x)=(-2+\sqrt{x-1})^{2}$

$f^{-1}(x)=x-3$

Correct answer:

$f^{-1}(x)=x^{2}+4x+5$

Explanation:

To find the inverse of a function, switch the x and y in the original function and then solve for y.

$f(x)=-2+\sqrt{x-1}$

$y=-2+\sqrt{x-1}$

$x=-2+\sqrt{y-1}$

$x+2=\sqrt{y-1}$

$(x+2)^{2}=(\sqrt{y-1})^{2}$

$(x+2)^{2}=y-1$

$y=(x+2)^{2}+1$

$y=x^{2}+4x+5$

Report an Error

Example Question #211 : Introduction To Functions

Find the inverse of y=3x-8 .

Possible Answers:

$y= \frac{1}{3}x + 8$

$y= \frac{1}{3}x + \frac{8}{3}$

y=-3x+8

$y=\frac{8}{3}x-\frac{8}{3}$

$y= \frac{1}{3}x - \frac{8}{3}$

Correct answer:

$y= \frac{1}{3}x + \frac{8}{3}$

Explanation:

In order to find the inverse, interchange the and variables.

y=3x-8

x=3y-8

Solve for . Add eight on both sides.

x+8=3y-8+8

x+8=3y

Divide by three on both sides.

$\frac{x+8}{3}=\frac{3y}{3}$

Simplify the left and right side.

The answer is: $y= \frac{1}{3}x+\frac{8}{3}$

Report an Error

Example Question #212 : Introduction To Functions

Find the inverse of: y=2(2-x)+2

Possible Answers:

$y= -\frac{1}{2}x + 3$

y=2x-6

$y= -\frac{1}{2}x + 6$

$y= -\frac{1}{2}x - 3$

$y= -\frac{1}{2}x - 6$

Correct answer:

$y= -\frac{1}{2}x + 3$

Explanation:

Interchange the and variables in the equation.

x=2(2-y)+2

Solve for . Subtract two on both sides.

x-2=2(2-y)

Distribute the right side of the equation to eliminate the parentheses.

x-2=4-2y

Subtract four on both sides.

x-6=-2y

Divide by negative two on both sides.

$\frac{x-6}{-2}=y$

Rewrite this in slope-intercept form.

The answer is: $y= -\frac{1}{2}x + 3$

Report an Error

Example Question #16 : Inverse Functions

If f(x) = 4x^2 , find $f^{-1}(x)$ .

Possible Answers:

$y=\pm \frac{4}{x^2}$

$y=\frac{x^2}{4}$

$y=\frac{1}{4x^2}$

$y=\pm \frac{\sqrt{x}}{4x}$

$y=\pm\frac{ \sqrt x}{2}$

Correct answer:

$y=\pm\frac{ \sqrt x}{2}$

Explanation:

The notation $f^{-1}(x)$ denotes the inverse of the function f(x) .

Rewrite f(x) using as a replacement of f(x) .

y=4x^2

Interchange and and solve for .

x=4y^2

Divide by four on both sides.

$\frac{x}{4}=y^2$

Square root both sides to eliminate the squared term.

$y=\pm \sqrt{\frac{x}{4}} = \pm\frac{ \sqrt x}{2}$

The answer is: $y=\pm\frac{ \sqrt x}{2}$

Report an Error

Example Question #17 : Inverse Functions

Find the inverse of y=.5x+2x-5

Possible Answers:

None of the answers.

$y=\frac{2(x+5)}{5}$

$y=\frac{-2(x+5)}{5}$

$y=\frac{5(x+2)}{2}$

$y=\frac{2(x-5)}{5}$

Correct answer:

$y=\frac{2(x+5)}{5}$

Explanation:

y=.5x+2x-5

Combine the x terms:

y=2.5x-5

Switch the variables:

x=2.5y-5

Solve for y:

x+5=2.5y

Convert y term to a fraction to see how to simplify more easily:

$x+5=\frac{5}{2}y$

$\mathbf{y=\frac{2(x+5)}{5}}$

Report an Error

Example Question #18 : Inverse Functions

Find the inverse function of $6x-\frac{2}{3}y=4$ .

Possible Answers:

$y=-\frac{1}{9}x+\frac{2}{3}$

None of these

$y=\frac{1}{9}x+\frac{2}{3}$

$y=\frac{x+6}{9}$

$y=\frac{x-9}{6}$

Correct answer:

$y=\frac{x+6}{9}$

Explanation:

$6x-\frac{2}{3}y=4$

First convert to slope intercept form:

y=9x-6

To find the inverse we switch the variables and solve for y again:

x=9y-6

x+6=9y

$\mathbf{y=\frac{x+6}{9}}$

Report an Error

Example Question #19 : Inverse Functions

Find the inverse function and simplify your solution:

f(x) = 3x + 21

Possible Answers:

$f^{-1}(x) = \frac{1}{3}x - 7$

$f^{-1}(x) = 3x-7$

$f^{-1}(x) = \frac{1}{3}x + 7$

$f^{-1}(x) = -3x - 21$

$f^{-1}(x) = x -21$

Correct answer:

$f^{-1}(x) = \frac{1}{3}x - 7$

Explanation:

To find the Inverse function of:

f(x) = 3x + 21

1. Replace f(x) with :

y = 3x + 21

2. Switch the variables and :

x = 3y + 21

3. Solve for :

$y = \frac{x - 21}{3}$

4. Simplify:

$y = \frac{1}{3}x - 7$

5. Replace with $f^{-1}(x)$ and the final solution is:

$f^{-1}(x) = \frac{1}{3}x - 7$

Report an Error

Example Question #19 : Inverse Functions

Find the inverse function and simplify your solution:

f(x) = 3x + 21

Possible Answers:

$f^{-1}(x) = \frac{1}{3}x - 7$

$f^{-1}(x) = 3x-7$

$f^{-1}(x) = \frac{1}{3}x + 7$

$f^{-1}(x) = -3x - 21$

$f^{-1}(x) = x -21$

Correct answer:

$f^{-1}(x) = \frac{1}{3}x - 7$

Explanation:

To find the Inverse function of:

f(x) = 3x + 21

1. Replace f(x) with :

y = 3x + 21

2. Switch the variables and :

x = 3y + 21

3. Solve for :

$y = \frac{x - 21}{3}$

4. Simplify:

$y = \frac{1}{3}x - 7$

5. Replace with $f^{-1}(x)$ and the final solution is:

$f^{-1}(x) = \frac{1}{3}x - 7$

Report an Error

Example Question #21 : Inverse Functions

Find the the inverse of f(x):

$f(x)=\frac{1}{5}x+2$

Possible Answers:

$f^{-1}(x)=5x-2$

$f^{-1}(x)=5x+10$

$f^{-1}(x)=10x+5$

$f^{-1}(x)=\frac{1}{5}x-2$

$f^{-1}(x)=5x-10$

Correct answer:

$f^{-1}(x)=5x-10$

Explanation:

To find an inverse of a function, switch x and y variables and solve:

$f^{-1}(x)=\frac{1}{5}x+2$

$x=\frac{1}{5}y+2$

Subtract 2 from both sides:

$x-2=\frac{1}{5}y$

Multiply both sides by 5:

5(x-2)=y

Distribute:

5x-10=y

The inverse is:

$f^{-1}(x)=5x-10$

Report an Error

Example Question #21 : Inverse Functions

Find the inverse of the following function:

$f(x)=\frac{6x+1}{x}, x>0$

Possible Answers:

$f^{-1}(x)=\frac{-6x-1}{-x}$

$f^{-1}(x)=\frac{1}{x-6}$

$f^{-1}(x)=\frac{1}{x+6}$

$f^{-1}(x)=0$

$f^{-1}(x)=-\frac{1}{x-6}$

Correct answer:

$f^{-1}(x)=\frac{1}{x-6}$

Explanation:

To find the inverse function of the function given, we must replace all of the x's with y's and, vice versa:

$x=\frac{6y+1}{y}$

Note that in the problem statement we were given f(x) and not , but they mean the same thing in the sense that is a function of .

Now, we just solve for y:

xy=6y+1

xy-6y=1

y(x-6)=1

$y=\frac{1}{x-6}$

To denote that this is the inverse of the original function, we can use the notation

$f^{-1}(x)=\frac{1}{x-6}$ .

Report an Error

View Algebra 2 Tutors

Katie
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor of Science, Economics.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Algebra 2 Tutors

Thien
Certified Tutor

University of Mary Washington, Bachelor of Science, Biology, General.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in New York City, Computer Science Tutors in Houston, SAT Tutors in Seattle, GMAT Tutors in Chicago, Statistics Tutors in Dallas Fort Worth, Algebra Tutors in Miami, Chemistry Tutors in Boston, SSAT Tutors in Philadelphia, Physics Tutors in Atlanta, English Tutors in Houston

Popular Courses & Classes

LSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Atlanta, SSAT Courses & Classes in Los Angeles, SAT Courses & Classes in Chicago, ISEE Courses & Classes in Boston, GRE Courses & Classes in Houston, SSAT Courses & Classes in Atlanta, SAT Courses & Classes in Denver, LSAT Courses & Classes in Denver, ISEE Courses & Classes in Atlanta

Popular Test Prep

GRE Test Prep in Chicago, LSAT Test Prep in Miami, ISEE Test Prep in Atlanta, GRE Test Prep in Washington DC, LSAT Test Prep in Phoenix, SAT Test Prep in San Diego, ACT Test Prep in Denver, MCAT Test Prep in Houston, MCAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Introduction to Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #13 : Inverse Functions

Example Question #211 : Introduction To Functions

Example Question #212 : Introduction To Functions

Example Question #16 : Inverse Functions

Example Question #17 : Inverse Functions

Example Question #18 : Inverse Functions

Example Question #19 : Inverse Functions

Example Question #19 : Inverse Functions

Example Question #21 : Inverse Functions

Example Question #21 : Inverse Functions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: