We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

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 #38 : Inverse Functions

Determine the inverse for the function: y=-2x-30

Possible Answers:

$y=-\frac{1}{2}x+15$

$y=-\frac{1}{2}x-15$

$y=\frac{1}{2}x-30$

$y=-\frac{1}{2}x-30$

y=-2x+15

Correct answer:

$y=-\frac{1}{2}x-15$

Explanation:

To find the inverse function, swap the x and y-variables.

x=-2y-30

Solve for y. Add 30 on both sides.

x+30=-2y-30+30

Simplify the right side.

x+30=-2y

Divide by negative two on both sides.'

$\frac{x+30}{-2}=\frac{-2y}{-2}$

Simplify both fractions.

The answer is: $y=-\frac{1}{2}x-15$

Report an Error

Example Question #231 : Functions And Graphs

Find the inverse function of the function below:

$f(x)=\frac{7x+3}{2x-1}$

Possible Answers:

$f^-^1(x)=\frac{2x-3}{7x+1}$

$f^-^1(x)=\frac{x+7}{2x-3}$

$f^-^1(x)=\frac{x+2}{7x-3}$

$f^-^1(x)=\frac{x+3}{2x-7}$

$f^-^1(x)=\frac{3x-7}{x+2}$

Correct answer:

$f^-^1(x)=\frac{x+3}{2x-7}$

Explanation:

To determine the inverse function f^-^1 of an explicitly defined function , substitute the dependent variable f(x)=y and independent variable for and respectively, and then solve the resultant equation for . This new equation will define the inverse function f^-^1 , provided that f(f^-^1(x))=x and f^-^1(f(x))=x for every in the domain of .

For this particular function, let denote the dependent variable f(x) :

$y=\frac{7x+3}{2x-1}$ .

Swap the variables and :

$x=\frac{7y+3}{2y-1}$ .

Let us now solve this equation for . Multiplying both sides by 2y-1 yields

2yx-x=7y+3 .

Subtracting the term and adding the term to both sides yields

2yx-7y=x+3 .

On the left-hand side of the equation, factor out from both terms using the distributive property to yield

y(2x-7)=x+3 .

Now divide both sides of the equation by 2x-7 to isolate the variable :

$y=\frac{x+3}{2x-7}$ .

In order to communicate the idea that this equation defines the inverse function to , let y=f^-^1(x) to yield the final answer:

$f^-^1(x)=\frac{x+3}{2x-7}$ .

To verify that this function is indeed the inverse of , calculate f(f^-^1(x)) and f^-^1(f(x)) .

$f(f^-^1(x))=\frac{7(\frac{x+3}{2x-7})+3}{2(\frac{x+3}{2x-7})-1}$

$=\frac{\frac{7x+21+6x-21}{2x-7}}{\frac{2x+6-2x+7}{2x-7}}$

$=\frac{13x}{13}$

$f^-^1(f(x))=\frac{(\frac{7x+3}{2x-1})+3}{2(\frac{7x+3}{2x-1})-7}$

$=\frac{\frac{7x+3+6x-3}{2x-1}}{\frac{14x+6-14x+7}{2x-1}}$

$=\frac{13x}{13}$

Hence, the inverse function of the function is

$f^-^1(x)=\frac{x+3}{2x-7}$

Report an Error

Example Question #41 : Inverse Functions

Determine the inverse of: y=9(6x-2)

Possible Answers:

$y=\frac{1}{54}x+18$

$y=-\frac{1}{54}x+\frac{1}{3}$

$y=\frac{1}{54}x+3$

$y=-\frac{1}{54}x+18$

$y=\frac{1}{54}x+\frac{1}{3}$

Correct answer:

$y=\frac{1}{54}x+\frac{1}{3}$

Explanation:

Interchange the x and y-variables and solve for y.

x=9(6y-2)

Distribute the nine through the binomial.

x=9(6y)+9(-2) = 54y-18

x= 54y-18

Add eighteen on both sides.

x+(18)= 54y-18+(18)

x+18=54y

Divide by 54 on both sides.

$\frac{x+18}{54}=\frac{54y}{54}$

The answer is: $y=\frac{1}{54}x+\frac{1}{3}$

Report an Error

Example Question #42 : Inverse Functions

Determine the inverse of y=2(9-2x) .

Possible Answers:

$y=-\frac{1}{4}x+9$

$y=-\frac{1}{4}x+18$

$y=\frac{1}{4}x+9$

$y=-\frac{1}{4}x-18$

$y=-\frac{1}{4}x+\frac{9}{2}$

Correct answer:

$y=-\frac{1}{4}x+\frac{9}{2}$

Explanation:

Interchange the x and y-variables and solve for y.

x=2(9-2y)

Distribute the integer through the binomial.

x=2(9-2y) = 18-4y

x= 18-4y

Add on both sides.

x+(4y)= 18-4y+(4y)

x+4y=18

Subtract on both sides.

4y=-x+18

Divide by four on both sides.

$\frac{4y}{4}=\frac{-x+18}{4}$

Simplify both sides.

The inverse is: $y=-\frac{1}{4}x+\frac{9}{2}$

Report an Error

Example Question #43 : Inverse Functions

Determine the inverse of: y=-3x-20

Possible Answers:

$y=-\frac{1}{3}x+\frac{20}{3}$

$y=3x+\frac{10}{3}$

$y=-\frac{1}{3}x-\frac{20}{3}$

$y=-\frac{1}{3}x+\frac{10}{3}$

$y=\frac{1}{3}x-\frac{20}{3}$

Correct answer:

$y=-\frac{1}{3}x-\frac{20}{3}$

Explanation:

Interchange the x and y-variable.

x=-3y-20

Add twenty on both sides.

x+20=-3y-20+20

x+20=-3y

Divide both sides by negative three.

$\frac{x+20}{-3}=\frac{-3y}{-3}$

Simplify both sides of the equation.

The answer is: $y=-\frac{1}{3}x-\frac{20}{3}$

Report an Error

Example Question #44 : Inverse Functions

Determine the inverse of y=-9x-5

Possible Answers:

$y= -9x+\frac{5}{9}$

$y= -\frac{1}{9}x+\frac{5}{9}$

$y= -\frac{1}{9}x-\frac{9}{5}$

$y= 9x+\frac{5}{9}$

$y= -\frac{1}{9}x-\frac{5}{9}$

Correct answer:

$y= -\frac{1}{9}x-\frac{5}{9}$

Explanation:

Interchange the x and y-values.

x=-9y-5

Solve for y. Add five on both sides.

x+(5)=-9y-5+(5)

The equation becomes: x+5 =-9y

Divide by negative nine on both sides.

$\frac{x+5}{-9} =\frac{-9y}{-9}$

The answer is: $y= -\frac{1}{9}x-\frac{5}{9}$

Report an Error

Example Question #45 : Inverse Functions

Determine the inverse: y=3(x-10)

Possible Answers:

$y=-\frac{1}{3}x-10$

$y=\frac{1}{3}x+30$

$y=\frac{1}{3}x+10$

$y=\frac{1}{3}x-10$

$y=-\frac{1}{3}x+30$

Correct answer:

$y=\frac{1}{3}x+10$

Explanation:

Interchange both the x and y- variables.

x=3(y-10)

Solve for y. Distribute the three through both terms of the binomial.

x=3y-30

Add 30 on both sides.

x+30=3y-30+30

x+30=3y

Divide by three on both sides.

$\frac{x+30}{3}=\frac{3y}{3}$

Simplify both sides.

The answer is: $y=\frac{1}{3}x+10$

Report an Error

Example Question #46 : Inverse Functions

Determine the inverse function: y=9x+26

Possible Answers:

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

$y=\frac{1}{9}x-\frac{26}{9}$

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

$y=-\frac{1}{9}x+\frac{26}{9}$

$y=-9x-\frac{26}{9}$

Correct answer:

$y=\frac{1}{9}x-\frac{26}{9}$

Explanation:

Interchange the x and y-variables.

x=9y+26

Solve for y. Subtract 26 from both sides.

x-26=9y+26-26

The equation becomes:

x-26=9y

Divide by nine on both sides.

$\frac{x-26}{9}=\frac{9y}{9}$

Simplify both fractions.

The answer is: $y=\frac{1}{9}x-\frac{26}{9}$

Report an Error

Example Question #41 : Inverse Functions

Determine the inverse of: y= 7x-4

Possible Answers:

$y=\frac{1}{7}x-\frac{4}{7}$

$y=\frac{4}{7}x-\frac{4}{7}$

$y=\frac{1}{7}x+\frac{4}{7}$

$y=-7x+\frac{4}{7}$

y=-7x+4

Correct answer:

$y=\frac{1}{7}x+\frac{4}{7}$

Explanation:

Interchange the x and y variables and solve for y.

x= 7y-4

Add four on both sides.

x+4= 7y-4+4

Simplify both sides.

x+4= 7y

Divide by seven on both sides.

$\frac{x+4}{7}= \frac{7y}{7}$

The answer is: $y=\frac{1}{7}x+\frac{4}{7}$

Report an Error

Example Question #48 : Inverse Functions

Determine the inverse of: y=-(x+6)

Possible Answers:

y=-6x

y=-x-6

y=x-6

y=-x+6

y=x+6

Correct answer:

y=-x-6

Explanation:

In order to determine the inverse, interchange the x and y-variables.

x=-(y+6)

Divide by negative one on both sides.

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

Simplify both sides.

-x = y+6

Subtract six from both sides.

-x-6 = y+6-6

The answer is: y=-x-6

Report an Error

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Algebra 2 Tutors

Sahibzada
Certified Tutor

Northwestern University, Bachelor of Science, Materials Engineering.

View Algebra 2 Tutors

Anthony
Certified Tutor

Purdue University-Main Campus, Bachelor of Science, Computer Engineering, General.

All Algebra II Resources

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

Popular Subjects

Spanish Tutors in Atlanta, Statistics Tutors in Los Angeles, ISEE Tutors in Los Angeles, SSAT Tutors in Chicago, Biology Tutors in San Diego, French Tutors in Phoenix, Computer Science Tutors in Phoenix, Spanish Tutors in Houston, Math Tutors in San Francisco-Bay Area, English Tutors in Phoenix

Popular Courses & Classes

GRE Courses & Classes in Atlanta, SAT Courses & Classes in Seattle, ISEE Courses & Classes in Miami, Spanish Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Atlanta, MCAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Washington DC, SSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Denver, SSAT Courses & Classes in New York City

Popular Test Prep

SSAT Test Prep in Philadelphia, GRE Test Prep in Atlanta, ISEE Test Prep in Boston, ACT Test Prep in San Diego, ACT Test Prep in Washington DC, GMAT Test Prep in Philadelphia, MCAT Test Prep in San Diego, SAT Test Prep in Washington DC, GRE Test Prep in San Diego, ACT Test Prep in Los Angeles

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 : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #38 : Inverse Functions

Example Question #231 : Functions And Graphs

Example Question #41 : Inverse Functions

Example Question #42 : Inverse Functions

Example Question #43 : Inverse Functions

Example Question #44 : Inverse Functions

Example Question #45 : Inverse Functions

Example Question #46 : Inverse Functions

Example Question #41 : Inverse Functions

Example Question #48 : Inverse Functions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: