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 #31 : Find The Inverse Of A Function

Find the inverse function of $\displaystyle f(x)=2x-3$.

Possible Answers:

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

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

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

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

None of the other answers.

Correct answer:

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

Explanation:

To find the inverse you must reverse the variables and solve for y.

Reverse the variables:

$\displaystyle f(x)=2x-3$

y=2x-3 $\displaystyle y=2x-3$

x=2y-3 $\displaystyle x=2y-3$

Solve for y:

x=2y-3 $\displaystyle x=2y-3$

x+3=2y $\displaystyle x+3=2y$

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

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

Report an Error

Example Question #41 : Inverse Functions

Are these two function inverses? $f(x)=\sqrt{x-4}$ $\displaystyle f(x)=\sqrt{x-4}$ and $\displaystyle g(x)=x^2+4$.

Possible Answers:

Cannot tell

Yes

F(x) does not have an inverse.

G(x) does not have an inverse.

Correct answer:

Yes

Explanation:

One can ascertain if two functions have an inverse by finding the composition of both functions in turn. Each composition should equal x if the functions are indeed inverses of each other.

$f(g(x))=\sqrt{x^2+4-4}=x$ $\displaystyle f(g(x))=\sqrt{x^2+4-4}=x$

$g(f(x))=(\sqrt{x-4})^2+4=x$ $\displaystyle g(f(x))=(\sqrt{x-4})^2+4=x$

The functions are inverses of each other.

Report an Error

Example Question #43 : Inverse Functions

Find the inverse of the following equation:

$\displaystyle y = 2(x+2)+2$

Possible Answers:

$y_{inv}= \frac{1}{4}(x-1)$ $\displaystyle y_{inv}= \frac{1}{4}(x-1)$

$y_{inv}= \frac{1}{2}(x-6)$ $\displaystyle y_{inv}= \frac{1}{2}(x-6)$

$y_{inv}= \frac{1}{2}(x-1)$ $\displaystyle y_{inv}= \frac{1}{2}(x-1)$

$y_{inv}= \frac{1}{3}(x-2)$ $\displaystyle y_{inv}= \frac{1}{3}(x-2)$

Correct answer:

$y_{inv}= \frac{1}{2}(x-6)$ $\displaystyle y_{inv}= \frac{1}{2}(x-6)$

Explanation:

To find the inverse of a function, replace the x any y positions:

Original Equation: $\displaystyle y = 2(x+2)+2$

Inversed Equation: $x = 2(y_{inv}+2)+2$ $\displaystyle x = 2(y_{inv}+2)+2$

Now solve for the inversed y value.

$x = 2(y_{inv}+2)+2$ $\displaystyle x = 2(y_{inv}+2)+2$

$\frac{x-2}{2} = y_{inv}+2$ $\displaystyle \frac{x-2}{2} = y_{inv}+2$

$y_{inv}=\frac{x-2}{2}-2 = \frac{1}{2}(x-6)$ $\displaystyle y_{inv}=\frac{x-2}{2}-2 = \frac{1}{2}(x-6)$

Report an Error

Example Question #37 : Find The Inverse Of A Function

Find the inverse of the following equation:

$y = \frac{1}{2}(x^2+4)$ $\displaystyle y = \frac{1}{2}(x^2+4)$

Possible Answers:

$y_{inv}=(2x+5)^\frac{1}{3}$ $\displaystyle y_{inv}=(2x+5)^\frac{1}{3}$

$y_{inv}=(x+5)^2$ $\displaystyle y_{inv}=(x+5)^2$

$y_{inv}=\sqrt{2x-4}$ $\displaystyle y_{inv}=\sqrt{2x-4}$

$y_{inv}=(2x+2)^2$ $\displaystyle y_{inv}=(2x+2)^2$

Correct answer:

$y_{inv}=\sqrt{2x-4}$ $\displaystyle y_{inv}=\sqrt{2x-4}$

Explanation:

To find the inverse of a function, replace the x any y positions:

Original Equation: $y = \frac{1}{2}(x^2+4)$ $\displaystyle y = \frac{1}{2}(x^2+4)$

Inversed Equation: $x = \frac{1}{2}(y_{inv}^2+4)$ $\displaystyle x = \frac{1}{2}(y_{inv}^2+4)$

Now solve for the inversed y value.

$x = \frac{1}{2}(y_{inv}^2+4)$ $\displaystyle x = \frac{1}{2}(y_{inv}^2+4)$

$2x =(y_{inv}^2+4)$ $\displaystyle 2x =(y_{inv}^2+4)$

$2x-4 =y_{inv}^2$ $\displaystyle 2x-4 =y_{inv}^2$

$y_{inv}=\sqrt{2x-4}$ $\displaystyle y_{inv}=\sqrt{2x-4}$

Report an Error

Example Question #42 : Inverse Functions

Find the inverse of the following equation:

$\displaystyle y = 2(x^3+12)+3$

Possible Answers:

$y_{inv}=(x-8)^\frac{1}{3}$ $\displaystyle y_{inv}=(x-8)^\frac{1}{3}$

$y_{inv}=(\frac{x-27}{2})^\frac{1}{3}$ $\displaystyle y_{inv}=(\frac{x-27}{2})^\frac{1}{3}$

$y_{inv}=(x-7)^2$ $\displaystyle y_{inv}=(x-7)^2$

$y_{inv}=(2x-12)^\frac{2}{3}$ $\displaystyle y_{inv}=(2x-12)^\frac{2}{3}$

Correct answer:

$y_{inv}=(\frac{x-27}{2})^\frac{1}{3}$ $\displaystyle y_{inv}=(\frac{x-27}{2})^\frac{1}{3}$

Explanation:

To find the inverse of a function, replace the x any y positions:

Original Equation: $\displaystyle y = 2(x^3+12)+3$

Inversed Equation: $x = 2(y_{inv}^3+12)+3$ $\displaystyle x = 2(y_{inv}^3+12)+3$

Now solve for the inversed y value.

$x = 2(y_{inv}^3+12)+3$ $\displaystyle x = 2(y_{inv}^3+12)+3$

$x-3 = 2(y_{inv}^3+12)$ $\displaystyle x-3 = 2(y_{inv}^3+12)$

$\frac{x-3}{2}= y_{inv}^3+12$ $\displaystyle \frac{x-3}{2}= y_{inv}^3+12$

$\frac{x-3}{2}-12= y_{inv}^3$ $\displaystyle \frac{x-3}{2}-12= y_{inv}^3$

$y_{inv}=(\frac{x-3}{2}-12)^\frac{1}{3} = (\frac{x-27}{2})^\frac{1}{3}$ $\displaystyle y_{inv}=(\frac{x-3}{2}-12)^\frac{1}{3} = (\frac{x-27}{2})^\frac{1}{3}$

Report an Error

Example Question #122 : Functions

Determine the inverse function, given

y=x^3+2 $\displaystyle y=x^3+2$

Possible Answers:

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

$y^{-1}=\sqrt[3]{x-2}$ $\displaystyle y^{-1}=\sqrt[3]{x-2}$

$y^{-1}=(x-2)^3$ $\displaystyle y^{-1}=(x-2)^3$

DNE $\displaystyle DNE$

Correct answer:

$y^{-1}=\sqrt[3]{x-2}$ $\displaystyle y^{-1}=\sqrt[3]{x-2}$

Explanation:

In order to find the inverse function we

switch the variables $\displaystyle x$ and $\displaystyle y$
solve for the new $\displaystyle y$ variable

For the function

y=x^3+2 $\displaystyle y=x^3+2$ ...

x=y^3+2 $\displaystyle x=y^3+2$

x-2=y^3 $\displaystyle x-2=y^3$

$y=\sqrt[3]{x-2}$ $\displaystyle y=\sqrt[3]{x-2}$

Hence, the inverse function is

$y^{-1}=\sqrt[3]{x-2}$ $\displaystyle y^{-1}=\sqrt[3]{x-2}$

Report an Error

View Pre-Calculus Tutors

Iffy
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Engineering, General. University of Maryland-College P...

View Pre-Calculus Tutors

Josephine
Certified Tutor

Philippine Normal College, Bachelor of Science, Mathematics Teacher Education. University of the Philippines, Master of Scien...

View Pre-Calculus Tutors

Ying
Certified Tutor

Iowa State University, Master of Science, Mathematics.

All Precalculus Resources

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

Popular Subjects

French Tutors in New York City, Biology Tutors in Denver, Statistics Tutors in New York City, SSAT Tutors in Dallas Fort Worth, Biology Tutors in Houston, Spanish Tutors in Washington DC, ACT Tutors in Phoenix, MCAT Tutors in Seattle, Spanish Tutors in Dallas Fort Worth, Chemistry Tutors in San Francisco-Bay Area

Popular Courses & Classes

SAT Courses & Classes in Houston, Spanish Courses & Classes in Phoenix, MCAT Courses & Classes in Atlanta, Spanish Courses & Classes in San Diego, LSAT Courses & Classes in Boston, ACT Courses & Classes in Chicago, SAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Los Angeles, GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Seattle

Popular Test Prep

SSAT Test Prep in Phoenix, ACT Test Prep in Phoenix, SAT Test Prep in Boston, SAT Test Prep in New York City, GMAT Test Prep in Miami, ACT Test Prep in Chicago, LSAT Test Prep in Seattle, MCAT Test Prep in New York City, ISEE Test Prep in Los Angeles, SSAT 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

Precalculus : Inverse Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #31 : Find The Inverse Of A Function

Example Question #41 : Inverse Functions

Example Question #43 : Inverse Functions

Example Question #37 : Find The Inverse Of A Function

Example Question #42 : Inverse Functions

Example Question #122 : Functions

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: