Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Inverses

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Matrices

Find the inverse of the following matrix, if possible.

$A=\begin{bmatrix} 4&-4 \\ -4&-4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} \frac{1}{8}&-\frac{1}{8} \\ -\frac{1}{8}& -\frac{1}{8} \end{bmatrix}$

$\begin{bmatrix} \frac{1}{4}&-\frac{1}{4} \\ -\frac{1}{4}& -\frac{1}{4} \end{bmatrix}$

The inverse does not exist.

$-\frac{1}{32}$

Correct answer:

$\begin{bmatrix} \frac{1}{8}&-\frac{1}{8} \\ -\frac{1}{8}& -\frac{1}{8} \end{bmatrix}$

Explanation:

Write the formula to find the inverse of a matrix.

$\begin{bmatrix} a&b\\ c&d \end{bmatrix}^-^1=\frac{1}{ad-bc}\begin{bmatrix} d& -b\\ -c& a \end{bmatrix}$

Substituting in the given matrix we are able to find the inverse matrix.

$\begin{bmatrix} 4&-4 \\ -4&-4 \end{bmatrix}^-^1=\frac{1}{(4)(-4)-(-4)(-4)}\begin{bmatrix} -4&4 \\ 4&4 \end{bmatrix}$

$\frac{1}{-32}\begin{bmatrix} -4&4 \\ 4&4 \end{bmatrix}=\begin{bmatrix} \frac{1}{8}&-\frac{1}{8} \\ -\frac{1}{8}& -\frac{1}{8} \end{bmatrix}$

Report an Error

Example Question #4 : Matrices

Find the inverse of the following matrix, if possible.

$A=\begin{bmatrix} 0&1 \\ 1&0 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 0&-1 \\-1&0 \end{bmatrix}$

The inverse does not exist.

$\begin{bmatrix} 1& 0\\ 0&1 \end{bmatrix}$

$\begin{bmatrix} 0& 1\\ 1&0 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 0& 1\\ 1&0 \end{bmatrix}$

Explanation:

Write the formula to find the inverse of a matrix.

$\begin{bmatrix} a&b\\ c&d \end{bmatrix}^-^1=\frac{1}{ad-bc}\begin{bmatrix} d& -b\\ -c& a \end{bmatrix}$

Using the given information we are able to find the inverse matrix.

$\begin{bmatrix} 0&1 \\ 1&0 \end{bmatrix}^-^1=\frac{1}{(0)(0)-(1)(1)}\begin{bmatrix} 0&-1 \\-1&0 \end{bmatrix}$

$-1\begin{bmatrix} 0&-1 \\ -1&0 \end{bmatrix}=\begin{bmatrix} 0& 1\\ 1&0 \end{bmatrix}$

Report an Error

Example Question #363 : Gre Subject Test: Math

Find the inverse of the function.

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

To find the inverse function, first replace g(x) with :

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

Now replace each with an and each with a :

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

Solve the above equation for :

x(2y-4)=y+3

2xy-4x=y+3

2xy-y=4x+3

(2x-1)y=4x+3

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

Replace with $g^{-1}(x)$ . This is the inverse function:

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

Report an Error

Example Question #3 : Find The Inverse Of A Relation

Find the inverse of the function y=2x^2+1 .

Possible Answers:

$f^-^1(x)=\pm \sqrt{\frac{x-1}{2}}$

$f^-^1(x)=\pm \sqrt{x-1}$

f^-^1(x)=x+1

$f^-^1(x)=\pm \sqrt{\frac{x+1}{2}}$

f^-^1(x)=-x+1

Correct answer:

$f^-^1(x)=\pm \sqrt{\frac{x-1}{2}}$

Explanation:

To find the inverse of y=2x^2+1 , interchange the and terms and solve for .

y=2x^2+1

x=2y^2+1

x-1=2y^2

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

$f^-^1(x)=\pm \sqrt{\frac{x-1}{2}}$

Report an Error

Example Question #364 : Gre Subject Test: Math

Find the inverse of the following equation.

$y=\sqrt{\ln(x)+2}$ .

Possible Answers:

y=e^x+2

y=x-2

$y=e^\pm ^{^{x^2}-2}$

$y=\pm x^2 -2$

$y=e^x^{^{2}-2}$

Correct answer:

$y=e^x^{^{2}-2}$

Explanation:

To find the inverse in this case, we need to switch our x and y variables and then solve for y.

Therefore,

$y=\sqrt{\ln(x)+2}$ becomes,

$x=\sqrt{\ln(y)+2}$

To solve for y we square both sides to get rid of the sqaure root.

$x^2=\ln(y)+2$

We then subtract 2 from both sides and take the exponenetial of each side, leaving us with the final answer.

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

$e^{x^2-2}=e^{\ln(y)}$

$e^x^{^{2}-2}=y$

Report an Error

Example Question #2 : Find The Inverse Of A Function

Find the inverse of the following function.

y=x^3+e^0

Possible Answers:

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

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

$y^{-1}=1-x^{3}}$

$y^{-1}=e^{0}}$

Correct answer:

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

Explanation:

To find the inverse of y, or

$y^{-1}$

first switch your variables x and y in the equation.

$x_{i}=y_i^3+e^0$

Second, solve for the variable y_i in the resulting equation.

x_i-e^0=y_i^3

$(x_i-e^0)^\frac{1}{3}=(y_i^{3})^\frac{1}{3}$

$y_i=\sqrt[3]{x_i-e^0}$

Simplifying a number with 0 as the power, the inverse is

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

Report an Error

Example Question #5 : Find The Inverse Of A Function

Find the inverse of the following function.

$y=\ln\, x\: +\: \pi$

Possible Answers:

$y^{-1}=\ln(y)-\pi$

$y^{-1}=\pi-\ln(x)$

Does not exist

$y^{-1}=e^{x-\pi}$

Correct answer:

$y^{-1}=e^{x-\pi}$

Explanation:

To find the inverse of y, or

$y^{-1}$

first switch your variables x and y in the equation.

$x_i=\ln(y_i)+\pi$

Second, solve for the variable y_i in the resulting equation.

$x_i-\pi=\ln\,y_i$

And by setting each side of the equation as powers of base e,

$y^{-1}=e^{x-\pi}$

Report an Error

Example Question #3 : Find The Inverse Of A Function

Find the inverse of the function.

y=x+5

Possible Answers:

$y^{-1}=-x-5$

$y^{-1}=x-5$

$y^{-1}=5-x$

$y^{-1}=5+x$

Correct answer:

$y^{-1}=x-5$

Explanation:

To find the inverse we need to switch the variables and then solve for y.

y=x+5

Switching the variables we get the following equation,

x=y+5 .

Now solve for y.

$y^{-1}=x-5$

Report an Error

Example Question #1 : Find The Inverse Of A Function

If $f(x)=-\frac{3x}{5}+11$ , what is its inverse function, $f^{-1}(x)$ ?

Possible Answers:

$f^{-1}(x)=-\frac{5x}{3}+\frac{55}{3}$

$f^{-1}(x)=-\frac{5x}{3}-\frac{55}{3}$

$f^{-1}(x)=-\frac{3x}{5}-\frac{33}{5}$

$f^{-1}(x)=-\frac{3x}{5}+\frac{33}{5}$

$f^{-1}(x)=\frac{5x}{3}+\frac{55}{3}$

Correct answer:

$f^{-1}(x)=-\frac{5x}{3}+\frac{55}{3}$

Explanation:

We begin by taking $f(x)=-\frac{3x}{5}+11$ and changing the f(x) to a , giving us $y=-\frac{3x}{5}+11$ .

Next, we switch all of our x's and y's , giving us $x=-\frac{3y}{5}+11$ .

Finally, we solve for by subtracting from each side, multiplying each side by , and dividing each side by , leaving us with,

$y=-\frac{5x}{3}+\frac{55}{3}$ .

Report an Error

Example Question #365 : Gre Subject Test: Math

Find $f^{-1}(x)$ for $f(x)=\frac{2x-7}{8x+3}$

Possible Answers:

$f^{-1}(x)=\sqrt{x^{2}+6}$

$f^{-1}(x)=\frac{2x+7}{4-3x}$

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

$f^{-1}(x)=\frac{3x+7}{2-8x}$

$f^{-1}(x)=\frac{3x^{2}+4x}{8}$

Correct answer:

$f^{-1}(x)=\frac{3x+7}{2-8x}$

Explanation:

$f(x)=\frac{2x-7}{8x+3}$

To find the inverse of a function, first swap the x and y in the given function.

$x=\frac{2y-7}{8y+3}$

Solve for y in this re-written form.

x(8y+3)=2y-7

8xy+3x=2y-7

8xy-2y=-7-3x

y(8x-2)=-7-3x

$y=\frac{-7-3x}{8x-2}$

$y=\frac{-(7+3x)}{-(-8x+2)}$

$y=\frac{3x+7}{2-8x}$

Report an Error

View Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

View Tutors

Samarth
Certified Tutor

Maharaja Sayajirao University of Baroda, Bachelor of Engineering, Mechanical Engineering. Concordia University-Seward, Master...

View Tutors

Max
Certified Tutor

SHAHiDBEHESHTiUNiVERSiTY, Bachelor of Science, Mathematics. SHAHiDBEHESHTiUNiVERSiTY, Master of Science, Mathematics.

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Denver, Statistics Tutors in Seattle, Statistics Tutors in New York City, Chemistry Tutors in Dallas Fort Worth, Physics Tutors in Atlanta, SSAT Tutors in Phoenix, ISEE Tutors in Atlanta, Biology Tutors in Boston, ACT Tutors in Denver, English Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Phoenix, SSAT Courses & Classes in Washington DC, ACT Courses & Classes in Atlanta, MCAT Courses & Classes in Washington DC, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in Miami, GMAT Courses & Classes in Boston, LSAT Courses & Classes in Boston, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Diego

Popular Test Prep

ISEE Test Prep in Boston, GMAT Test Prep in San Diego, SSAT Test Prep in Seattle, GMAT Test Prep in Miami, MCAT Test Prep in Washington DC, GMAT Test Prep in Philadelphia, SSAT Test Prep in New York City, GMAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Atlanta, 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

GRE Subject Test: Math : Inverses

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #3 : Matrices

Example Question #4 : Matrices

Example Question #363 : Gre Subject Test: Math

Example Question #3 : Find The Inverse Of A Relation

Example Question #364 : Gre Subject Test: Math

Example Question #2 : Find The Inverse Of A Function

Example Question #5 : Find The Inverse Of A Function

Example Question #3 : Find The Inverse Of A Function

Example Question #1 : Find The Inverse Of A Function

Example Question #365 : Gre Subject Test: Math

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: