We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Functions and Graphs

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 #23 : Inverse Functions

What is the inverse function of $f(x)=\frac{x^2 + 4x + 3}{x + 1}$ ?

Possible Answers:

$\frac{x+1}{x^2 + 4x + 3}$

x-3

$\frac{1}{x-1}$

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

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

Correct answer:

x-3

Explanation:

Before we begin, it would help to try and simplify the problem. Let's start by factoring the numerator:

x^2 + 4x + 3 = (x+1)(x+3)

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

We can see that the (x+1) terms will cancel, making this problem much easier:

f(x)= x+3

To find the inverse, we can put a where the is currently, put a for the f(x) , and then solve for .

x = y + 3

y = x-3

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

Report an Error

Example Question #741 : Algebra Ii

Find the inverse of $f(x)= \frac{4}{x^2 +3}$ .

Possible Answers:

$3-\sqrt{\frac{4}{x}}$

$\pm\sqrt{\frac{4}{x}-3}$

4(x+2)^2

$\frac{x^{2}+3}{4}$

$\frac{4}{(x+3)(x-1)}$

Correct answer:

$\pm\sqrt{\frac{4}{x}-3}$

Explanation:

First we're going to change the in the function to a , set the function equal to , and solve for :

$x=\frac{4}{y^2 + 3}$

Multiply each side by y^2 + 3 :

x(y^2 + 3)=4

Divide each side by :

$y^2 + 3=\frac{4}{x}$

Subtract from each side:

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

Finally, take the square root of each side:

$y=\pm\sqrt{\frac{4}{x}-3}$

Report an Error

Example Question #742 : Algebra Ii

Find the inverse of the given function:

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

Possible Answers:

$\frac{3+x}{x+1}$

$\frac{3-x}{x-1}$

$\frac{y+3}{y+1}$

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

Correct answer:

$\frac{3-x}{x-1}$

Explanation:

To find the inverse of the function, we must first replace all x in the equation with y, and all y in the equation with x:

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

Now, solve for y:

x(y+1)=y+3

xy+x=y+3

xy-y=3-x

y(x-1)=3-x

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

Report an Error

Example Question #26 : Inverse Functions

Find the inverse function of f(x)=x^3-1 .

Possible Answers:

$y=\sqrt[3]{x+1}$

$y=\sqrt[3]{-x+1}$

$y=\sqrt[3]{x-1}$

There is no inverse for f(x)

Correct answer:

$y=\sqrt[3]{x+1}$

Explanation:

Step 1: To find the inverse of a function f(x) , we will first switch the places of x and y. Wherever we saw y, we put x. Where we see x, we put y.

y=x^3+1

After changing places of letters:

x=y^3+1

Step 2: We want to solve for y, so we ned to get rid of the on the right side.

x-1=y^3

Step 3: We want to find , but we have y^3 . To find , we will take the cube root of both sides

$\sqrt[3]{x-1}=\sqrt[3]{y^3}$

This simplifies to:

$\sqrt[3]{x-1}=y$

The inverse function of f(x) is $\sqrt[3]{x-1}=y$

Report an Error

Example Question #221 : Functions And Graphs

What is the inverse for the function $y=\frac{x-7}{8}$

Possible Answers:

y=8x+7

y=8x-7

$y=\frac{8}{x-7}$

y=x+7

Inverse does not exist

Correct answer:

y=8x+7

Explanation:

To find the inverse of a function switch the position of x and y and solve to y.

$x=\frac{y-7}{8}\Rightarrow8x=y-7\Rightarrow8x+7=y$

Report an Error

Example Question #28 : Inverse Functions

Find the inverse of: y=4(x-6)

Possible Answers:

y=-4x+24

$y=\frac{1}{4}x+\frac{2}{3}$

$y=-\frac{1}{4}x+6$

y=-4x-24

$y=\frac{1}{4}x+6$

Correct answer:

$y=\frac{1}{4}x+6$

Explanation:

Interchange the x and y-variables.

x=4(y-6)

Solve for y. Distribute the constant through the binomial.

x=4y-24

Add 24 on both sides.

x+24=4y-24+24

The equation becomes:

x+24=4y

Divide by four on both sides.

$\frac{x+24}{4}=\frac{4y}{4}$

Simplify both sides.

The answer is: $y=\frac{1}{4}x+6$

Report an Error

Example Question #29 : Inverse Functions

Find $f^{-1}(x)$ if f(x)= 9x-3 .

Possible Answers:

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

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

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

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

$y=\sqrt{9x-3}$

Correct answer:

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

Explanation:

To solve for the inverse function, first replace f(x) with .

The equation becomes: y= 9x-3

Interchange the variables.

x=9y-3

Add three on both sides.

x+3=9y

Divide by nine on both sides.

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

Simplify both sides of the equation.

The answer is: $y=\frac{1}{9}x+\frac{1}{3}$

Report an Error

Example Question #22 : Inverse Functions

Find the inverse of the function: $y=-\frac{1}{4}x-6$

Possible Answers:

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

y=-4x-24

y=-4x+24

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

$\textup{The inverse is not given.}$

Correct answer:

y=-4x-24

Explanation:

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

$x=-\frac{1}{4}y-6$

Solve for y. Add 6 on both sides of the equation.

$x+6=-\frac{1}{4}y-6+6$

The equation becomes:

$x+6=-\frac{1}{4}y$

Multiply by negative four on both sides to isolate the y-variable.

$-4(x+6)=-4(-\frac{1}{4}y)$

Simplify both sides of the equation.

The answer is: y=-4x-24

Report an Error

Example Question #31 : Inverse Functions

Find the inverse of the equation: y=6x-14

Possible Answers:

y=-6x-14

$y=\frac{1}{6}x -\frac{7}{3}$

$y=\frac{1}{6}x +\frac{7}{3}$

$y=-\frac{1}{6}x -\frac{7}{3}$

y=6x-14

Correct answer:

$y=\frac{1}{6}x +\frac{7}{3}$

Explanation:

To solve for the inverse, first interchange the x and y-variables.

x=6y-14

Solve for y. Add 14 on both sides.

x+14=6y-14+14

Simplify the right side.

x+14=6y

Divide by six on both sides.

$\frac{x+14}{6}=\frac{6y}{6}$

Simplify both sides of the equation.

The answer is: $y=\frac{1}{6}x +\frac{7}{3}$

Report an Error

Example Question #32 : Inverse Functions

Find the inverse of the following function: $y=-\frac{2}{3}x+2$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Interchange the x and y-variables.

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

Solve for y. Subtract two from both sides.

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

Simplify the right side.

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

Multiply both sides by the reciprocal of the coefficient in front of the y-variable.

$-\frac{3}{2}(x-2)=-\frac{2}{3}y\cdot -\frac{3}{2}$

Simplify both sides. Distribute the fraction on the left side.

$y=-\frac{3}{2}x-2(-\frac{3}{2})$

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

Report an Error

View Algebra 2 Tutors

Robert
Certified Tutor

University of Pittsburgh, Bachelor of Science, Physics.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Algebra 2 Tutors

Tom
Certified Tutor

University of Wisconsin-Madison, Bachelor of Science, Atmospheric Sciences and Meteorology. Embry-Riddle Aeronautical Univers...

All Algebra II Resources

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

Popular Subjects

English Tutors in Atlanta, Spanish Tutors in Atlanta, English Tutors in Washington DC, Computer Science Tutors in Philadelphia, GRE Tutors in Houston, LSAT Tutors in Dallas Fort Worth, Chemistry Tutors in Washington DC, Reading Tutors in San Diego, Statistics Tutors in Philadelphia, LSAT Tutors in San Francisco-Bay Area

Popular Courses & Classes

ACT Courses & Classes in Chicago, ACT Courses & Classes in Atlanta, SAT Courses & Classes in Seattle, SAT Courses & Classes in San Diego, MCAT Courses & Classes in Atlanta, GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in New York City, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Boston, MCAT Courses & Classes in Philadelphia

Popular Test Prep

ACT Test Prep in Chicago, ISEE Test Prep in New York City, GMAT Test Prep in Philadelphia, MCAT Test Prep in Chicago, SSAT Test Prep in Houston, ISEE Test Prep in San Francisco-Bay Area, MCAT Test Prep in Atlanta, MCAT Test Prep in Washington DC, MCAT Test Prep in Denver, GMAT Test Prep in Seattle

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 : Functions and Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #23 : Inverse Functions

Example Question #741 : Algebra Ii

Example Question #742 : Algebra Ii

Example Question #26 : Inverse Functions

Example Question #221 : Functions And Graphs

Example Question #28 : Inverse Functions

Example Question #29 : Inverse Functions

Example Question #22 : Inverse Functions

Example Question #31 : Inverse Functions

Example Question #32 : Inverse Functions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: