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 #2 : Inverse Functions

$g^{-1}(2)=6$

g(3)=4

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

f(3)=6

$f^{-1}(9)=2$

What is $f\circ g\circ f^{-1}(6)$ ?

Possible Answers:

Correct answer:

Explanation:

The question is essentially asking this: take $f^{-1}(6)$ say that equals , then take g(a) , then whatever that equals, say , take f(b) . So, we start with $f^{-1}(6)$ ; we know that f(3)=6 , so if we flip that around we know $f^{-1}(6)=3$ . Now we have to take g(3) , but we know that is . Now we have to take f(4) , but we don't have that in our table; we do have $f^{-1}(-2)=4$ , though, and if we flip it around, we get f(4)=-2 , which is our answer.

Report an Error

Example Question #3 : Inverse Functions

$g^{-1}(2)=6$

g(3)=4

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

f(3)=6

$f^{-1}(9)=2$

What is $g\circ f\circ g^{-1}(4)$ ?

Possible Answers:

Correct answer:

Explanation:

Our question is asking "What is of of inverse?" First we find the inverse of . Looking at the question, we see g(3)=4 ; if we flip that around, we get $g^{-1}(4)=3$ . Now we need to find what f(3) is; that is an easy one, as it is directly provided: f(3)=6 . Now we need to find g(6) . Again, this isn't given, but what is given is $g^{-1}(2)=6$ , so g(6)=2 , and that is our answer.

Report an Error

Example Question #4 : Inverse Functions

Over which line do you flip a function when finding its inverse?

Possible Answers:

y=-x

y=0

You do not flip a function over a line when finding its inverse.

y=x

x=0

Correct answer:

y=x

Explanation:

To find the inverse of a function, you need to change all of the values to values and all the values to values. If you flip a function over the line y=x , then you are changing all the values to values and all the values to values, giving you the inverse of your function.

Report an Error

Example Question #5 : Inverse Functions

Find the inverse of this function:

$f(x)=e^{x^2-3}+\pi$

Possible Answers:

$ln(x^2-\pi+3)$

$\pm\sqrt{x-\pi}+ln(3)$

$(cos(x-\pi)+3)^2$

$\pm\sqrt{ln(x-\pi)+3}$

$\frac{1}{e^{x^2-3}+\pi}$

Correct answer:

$\pm\sqrt{ln(x-\pi)+3}$

Explanation:

To find the inverse of a function, we need to switch all the inputs ( variables) for all the outputs ( f(x) variables or variables), so if we just switch all the variables to variables and all the f(x) variables to variables and solve for , then will be our inverse function.

$f(x)=e^{x^2-3}+\pi$

turns into the following once the variables are switched:

$x=e^{y^2-3}+\pi$

the first thing we do is subtract $\pi$ from each side; then, we take the natural log of each side. This gives us

$ln(x-\pi)=y^2-3$

Then we just add three to each side and take the square root of each side, making sure we have both the positive and negative roots.

$\pm\sqrt{ln(x-\pi)+3}=y$

This is the inverse function of the function with which we were provided.

Report an Error

Example Question #1 : Inverse Functions

Please find the inverse of the following function.

y=4x-9

Possible Answers:

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

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

y = 4x + 9

y = -4x + 9

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

Correct answer:

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

Explanation:

In order to find the inverse function, we must swap and and then solve for .

y = 4x-9

Becomes

x=4y-9

Now we need to solve for :

$x+\underset{+9}{0}=4y-\underset{+9}{9}$

Finally, we need to divide each side by 4.

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

This gives us our inverse function:

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

Report an Error

Example Question #1 : Inverse Functions

Find the inverse of y=3x+3 .

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

To create the inverse, switch x and y making the solution x=3y+3.

y must be isolated to finish the problem.

Report an Error

Example Question #1 : Inverse Functions

$f(x) = x^{3} -5$

Which one of the following functions represents the inverse of $f\left ( x \right )?$

A) x-5

B) $\sqrt[3]{x^{3}-5}$

C) $\sqrt[3]{x+5}$

D) $x^{3 } + 5$

E) $x^{3} - 5$

Possible Answers:

Correct answer:

Explanation:

Given $y = x^{3} - 5$

Hence $x^{3}=y+5$

Interchanging with we get:

$y^{3}=x+5$

Solving for results in $y=\sqrt[3]{x+5}$ .

Report an Error

Example Question #1 : Inverse Functions

What is the inverse of $y=\frac{2}{5}x -3$ ?

Possible Answers:

$y=\frac{5}{2}x +3$

$y=-\frac{5}{2}x+\frac{15}{2}$

$y=\frac{5}{2}x+\frac{15}{2}$

$y=\frac{5}{2}x-\frac{15}{2}$

$y=\frac{5}{2}x+15$

Correct answer:

$y=\frac{5}{2}x+\frac{15}{2}$

Explanation:

Interchange the and variables and solve for .

$x=\frac{2}{5}y -3$

$x+3=\frac{2}{5}y$

5x+15=2y

$y=\frac{5}{2}x+\frac{15}{2}$

Report an Error

Example Question #11 : Inverse Functions

Inverse Functions

Given the function f(x) below, find its inverse:

f(x)=3x-5

Possible Answers:

$f^{^{-1}}(x)=\frac{1}{3}x-5$

$f^{^{-1}}(x)=5x-3$

$f^{^{-1}}(x)=3x+5$

$f^{^{-1}}(x)=\frac{1}{3}x+\frac{5}{3}$

Correct answer:

$f^{^{-1}}(x)=\frac{1}{3}x+\frac{5}{3}$

Explanation:

When finding the inverse go through the following steps:

1) Replace f(x) with y:

y=3x-5

2) Swap the x and y variables

x=3y-5

3) Solve for y:

x+5=3y add 5 to both sides

x/3+5/3=3y/3 divide everything by 3

$f^{^{-1}}(x)=\frac{1}{3}x+\frac{5}{3}$ simplify and express as an inverse using $f^{-1}(x)$

Report an Error

Example Question #11 : Inverse Functions

Find the inverse of .

y=3x^2+7

Possible Answers:

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

$y^{-1}=3\sqrt{x}+7$

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

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

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

Correct answer:

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

Explanation:

To find the inverse of a function, swap the x and y variable and solve for y.

The new expression after the swap is x=3y^2+7

Now solve for y.

3y^2=x-7

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

$y=\pm\sqrt{\frac{x-7}{3}}$

This y actually represents the inverse of the original y.

Report an Error

View Algebra 2 Tutors

John
Certified Tutor

Arizona State University, Bachelor of Science, Microbiology.

View Algebra 2 Tutors

Lawrence
Certified Tutor

Harvey Mudd College, Bachelor of Engineering, Engineering, General. UC Berkeley, Master's/Graduate, Engineering.

View Algebra 2 Tutors

Philipp
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mechanical Engineering.

All Algebra II Resources

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

Popular Subjects

English Tutors in Miami, MCAT Tutors in Chicago, Math Tutors in Washington DC, Math Tutors in Miami, Reading Tutors in New York City, Math Tutors in New York City, Spanish Tutors in Los Angeles, Statistics Tutors in Miami, French Tutors in San Francisco-Bay Area, GMAT Tutors in Los Angeles

Popular Courses & Classes

SAT Courses & Classes in Phoenix, ACT Courses & Classes in Seattle, LSAT Courses & Classes in Atlanta, MCAT Courses & Classes in Miami, ACT Courses & Classes in Philadelphia, SAT Courses & Classes in Boston, Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Boston, ISEE Courses & Classes in Houston

Popular Test Prep

GRE Test Prep in Los Angeles, LSAT Test Prep in Los Angeles, ISEE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Denver, LSAT Test Prep in San Diego, LSAT Test Prep in Miami, ISEE Test Prep in Chicago, GMAT Test Prep in Miami, ISEE Test Prep in Boston, GRE Test Prep in Philadelphia

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 #2 : Inverse Functions

Example Question #3 : Inverse Functions

Example Question #4 : Inverse Functions

Example Question #5 : Inverse Functions

Example Question #1 : Inverse Functions

Example Question #1 : Inverse Functions

Example Question #1 : Inverse Functions

Example Question #1 : Inverse Functions

Example Question #11 : Inverse Functions

Example Question #11 : Inverse Functions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: