We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Inverse Functions

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Inverse Functions

Find the inverse of y = x +4 .

Possible Answers:

x = y - 4

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

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

x=4-y

y = x - 4

Correct answer:

y = x - 4

Explanation:

To find the inverse of the function, we simply need to switch the values of and and solve for .

y = x+4

Switching and , we can write the function as:

x = y+4

We now subtract to solve for :

x - 4 = y

y = x -4

Report an Error

Example Question #22 : Inverse Functions

Find the inverse of y = 3x -7 .

Possible Answers:

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

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

x=7(3y)

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

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

Correct answer:

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

Explanation:

To find the inverse of this function, we switch and in the function:

y =3x -7

x = 3y -7

We now solve for :

x + 7 = 3y

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

Report an Error

Example Question #21 : Inverse Functions

Find the inverse of y = x^2 - 2 .

Possible Answers:

$y= \sqrt{x+2}$

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

$y=x\pm\sqrt2$

$y = \sqrt x + 2$

x = y^2+2

Correct answer:

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

Explanation:

To find the inverse of this function we can switch the and variables and solve for .

First, switch and in the function:

y = x^2 -2

x = y^2-2

Now, solve for :

x + 2 = y^2

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

Report an Error

Example Question #12 : Find The Inverse Of A Function

Find the inverse of $y = \sqrt{x+3}$ .

Possible Answers:

y = x^2 + 3

x = y^2+3

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

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

y = x^2 - 3

Correct answer:

y = x^2 - 3

Explanation:

To find the inverse of the function, we switch and in the function.

$y = \sqrt{x+3}$

$x = \sqrt{y+3}$

We can now find our answer by solving for :

x^2 = y+3

y = x^2-3

Report an Error

Example Question #21 : Inverse Functions

Find the inverse of y = x^3 +3 .

Possible Answers:

y=3x-3

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

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

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

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

Correct answer:

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

Explanation:

To find the inverse of the function, we swtich and in the function.

y = x^3 +3

x = y^3 +3

Solve for :

x - 3 = y^3

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

Report an Error

Example Question #1057 : Pre Calculus

Find the inverse of this function: g(x)=(2x)^5

Possible Answers:

$g^{-1}(x)=\left({\frac{1}{2}x}\right)^{0.2}$

$g^{-1}(x)=5 \sqrt x$

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

$g^{-1}(x)= \frac{x^{0.2}}{2}$

$g^{-1}(x)=\sqrt[5]{2x}$

Correct answer:

$g^{-1}(x)= \frac{x^{0.2}}{2}$

Explanation:

In order to have the inverse of a function, the new function must perform the inverse opperations in the opposite order. One way to ensure that is true is to consider the case of y=g(x) , switch x and y, then solve for y.

y=(2x)^5 in this case becomes x = (2y)^5 .

Our first step in solving is to take the reciprocal power on each side.

The reciprocal of 5 is $\frac{1}{5}=0.2$ , so we'll take both sides to the power of 0.2:

$x^{0.2}= 2y$ Now divide by 2:

$\frac{x^{0.2}}{2}=y$

Note that the answer $g^{-1}(x)=\left({\frac{1}{2}x}\right)^{0.2}$ has the correct inverse opperations, it is just in the wrong order - first you divide by 2, then you take x to the power of 0.2.

Report an Error

Example Question #21 : Inverse Functions

Find the inverse of this function: $h(x)=\sqrt{\frac{1}{x}}+1$

Possible Answers:

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

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

$h^{-1}(x)=-(x-1)^2$

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

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

Correct answer:

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

Explanation:

In order to have the inverse of a function, the new function must perform the inverse opperations in the opposite order. One way to ensure that is true is to consider the case of y=h(x) , switch x and y, then solve for y.

In this case, $y=\sqrt{\frac{1}{x}}+1$ becomes $x=\sqrt{\frac{1}{y}}+1$ and we solve for y.

$x=\sqrt{\frac{1}{y}}+1$ subtract 1 from both sides

$x-1 = \sqrt{\frac{1}{y}}$ square both sides

$(x-1)^2 = \frac{1}{y}$ now we will take both sides to the power of -1, in other words flip each side to the reciprocal.

We can consider (x-1)^2 to be $\frac{(x-1)^2}{1}$

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

Report an Error

Example Question #102 : Functions

Find the inverse of the follow function:

y=3x^2-9

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

To find the inverse, substitute all x's for y's and all y's for x's and then solve for y.

x=3y^2-9

x+9=3y^2

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

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

Report an Error

Example Question #21 : Find The Inverse Of A Function

Find the inverse function.

Find the inverse function $f^{^{-1}}(x)$ of the function $f(x)=\frac{3x-4}{2}$

Possible Answers:

$f^{-1}(x)= \frac{3x+4}{2}$

$f^{-1}(x)=\frac{2x+4}{3}$

None of these answers are correct.

$f^{-1}(x)= \frac{2x-3}{4}$

$f^{-1}(x)= \frac{2x-4}{3}$

Correct answer:

$f^{-1}(x)=\frac{2x+4}{3}$

Explanation:

To find an inverse function, switch x and y variables and solve again for y. The new function is the inverse. f(x) can be called y. To check your answer, you can insert either function into the x variable of the other, and the equations should both solve to equal x.

$f(x)= \frac{3x-4}{2}$

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

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

2x= 3y-4

2x+4=3y

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

$\frac {2x+4}{3} = f^{-1}(x)$

Report an Error

Example Question #104 : Functions

Find the inverse of this function:

y=x^2 +6x + 9

Possible Answers:

y= (x+3)^2

y=(x-3)^2

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

$y=3+\sqrt{x}$

y=9+x

Correct answer:

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

Explanation:

To find the inverse of a function like this, switch the x and y variables (thereby "inverting" the function) and then solve for x.

First we would set up:

x=y^2 +6y + 9

And then let's factor:

x=(y+3)^2

And take the square root of both sides:

$\pm \sqrt{x} = y+3$

Leaving us with the final answer:

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

Report an Error

View Pre-Calculus Tutors

Michael
Certified Tutor

St. Francis College, Bachelor of Science, Mathematics. St John's University-New York, Master of Science, Education.

View Pre-Calculus Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Pre-Calculus Tutors

Olivia
Certified Tutor

University of St. Andrews, Bachelor, Earth & Environmental Science.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SSAT Tutors in Denver, Computer Science Tutors in Chicago, French Tutors in San Francisco-Bay Area, Reading Tutors in Atlanta, GRE Tutors in Dallas Fort Worth, GRE Tutors in San Francisco-Bay Area, GRE Tutors in Seattle, Calculus Tutors in San Diego, Statistics Tutors in Washington DC, Physics Tutors in Los Angeles

Popular Courses & Classes

GMAT Courses & Classes in Denver, GRE Courses & Classes in Miami, Spanish Courses & Classes in Miami, GMAT Courses & Classes in New York City, LSAT Courses & Classes in Denver, LSAT Courses & Classes in New York City, ACT Courses & Classes in Phoenix, MCAT Courses & Classes in Chicago, SAT Courses & Classes in Washington DC, SAT Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in Phoenix, SAT Test Prep in New York City, GMAT Test Prep in Atlanta, SSAT Test Prep in Atlanta, SAT Test Prep in Los Angeles, SSAT Test Prep in Boston, MCAT Test Prep in Seattle, ISEE Test Prep in Houston, LSAT Test Prep in Philadelphia, GMAT Test Prep in New York City

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

Precalculus : Inverse Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #21 : Inverse Functions

Example Question #22 : Inverse Functions

Example Question #21 : Inverse Functions

Example Question #12 : Find The Inverse Of A Function

Example Question #21 : Inverse Functions

Example Question #1057 : Pre Calculus

Example Question #21 : Inverse Functions

Example Question #102 : Functions

Example Question #21 : Find The Inverse Of A Function

Example Question #104 : Functions

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: