Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to find inverse variation

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find Inverse Variation

Find the inverse of the following function:

$f(x) = x^{2}-3$

Possible Answers:

$x^{2} -3$

$x^{2} +3$

None because the given function is not one-to-one.

$\sqrt{x+3}$

$-\sqrt{x+3}$

Correct answer:

None because the given function is not one-to-one.

Explanation:

$f\left ( x \right ) = x^{2}-3$

which is the same as

$y = x^{2}-3$

If we solve for we get

$x^{2} = y +3$

Taking the square root of both sides gives us the following:

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

Interchanging and gives us

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

Which is not one-to-one and therefore not a function.

Report an Error

Example Question #1 : How To Find Inverse Variation

Given

$f\left ( x \right ) = 2x+3$

and

$g\left ( x \right ) = \frac{x-3}{2}$ .

Find $f\left ( g\left ( x \right ) \right )$ .

Possible Answers:

$g\left ( x \right )$

$f\left ( x \right )$

Correct answer:

Explanation:

Starting with $f\left ( x \right ) = 2x+3$

Replace with $g\left ( x \right )$ .

We get the following:

$2\left ( \frac{x-3}{2} \right )+3=x-3+3$

Which is equal to .

Report an Error

Example Question #2 : How To Find Inverse Variation

Given:

f(x)=2x+3

and

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

Find g(f(x)) .

Possible Answers:

f(x)

g(x)

x+y

Correct answer:

Explanation:

Start with g(x) which is equal to

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

and then replace with f(x) . We get the following:

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

which is equal to

$\frac{2x}{2}=x$

Report an Error

Example Question #2 : How To Find Inverse Variation

Which of the following is not a one-to-one function?

$f\left ( x \right ) = 2x + 5$
$f\left ( x \right ) = 2^{-x}$
$f\left ( x \right ) = x^{3} + 5$
$f\left ( x \right ) = \pm \sqrt{x+3}$
$f\left ( x \right ) = x^{5}$

Possible Answers:

Correct answer:

Explanation:

Expression 4 is not even a function because for any value of , one gets two values of violating the definition of a function. If it is not a function, then it can not be an one-to-one function.

Report an Error

Example Question #3 : How To Find Inverse Variation

f(x) is a one-to-one function specified in terms of a set of $\left ( x,y \right )$ coordinates:

A = $\left \{ \left ( 0,0 \right ), \left ( 1,2\right ),\left ( 2,4 \right ), \left ( 3,6 \right )\right \}$

Which one of the following represents the inverse of the function specified by set A?

B = $\left \{ \left ( 0,0 \right ), \left ( 0,1 \right ), \left ( 0,2 \right ), \left ( 0,3 \right ) \right \}$

C = $\left \{ \left ( 0,0 \right ), \left ( 2,1 \right ), \left ( 4,2 \right ), \left ( 6,3 \right ) \right \}$

D = $\left \{ \left ( 1,1 \right ), \left ( 2,1 \right ), \left ( -2,1 \right ), \left ( 3,1 \right ) \right \}$

E = $\left \{ \left ( -2,1 \right ), \left ( -2,5 \right ), \left ( -2,3 \right ), \left ( -2, -2 \right ) \right \}$

F = $\left \{ \left ( 2,0 \right ), \left ( 2,-3 \right ),\left ( 2,5 \right ), \left ( 2,-7 \right ) \right \}$

Possible Answers:

Set E

Set F

Set C

Set D

Set B

Correct answer:

Set C

Explanation:

The set A is an one-to-one function of the form

f(x) = 2x

One can find $f^{-1}\left ( x \right )$ by interchanging the and coordinates in set A resulting in set C.

Report an Error

Example Question #1 : How To Find Inverse Variation

varies directly with , and inversely with the square root of .

If y=6 and z =64 , then x = 10 .

Find if y=9 and z=144 .

Possible Answers:

$8\tfrac{1}{3}$

$6\tfrac{2}{3}$

$12\tfrac{1}{2}$

$4\tfrac{4}{9}$

Correct answer:

Explanation:

The variation equation can be written as below. Direct variation will put in the numerator, while inverse variation will put $\sqrt{z}$ in the denominator. is the constant that defines the variation.

$x=k* \frac{y}{\sqrt{z}}$

To find constant of variation, , substitute the values from the first scenario given in the question.

$10=k* \frac{6}{\sqrt{64}}=k* \frac{6}{8}=k* \frac{3}{4}$

$k=10\div\frac{3}{4}}= \frac{40}{3}$

We can plug this value into our variation equation.

$x=\frac{40}{3}\cdot \frac{y}{\sqrt{z}}$

Now we can solve for given the values in the second scenario of the question.

$x=\frac{40}{3}* \frac{9}{\sqrt{144}}=\frac{40}{3}* \frac{9}{12}=10$

Report an Error

Example Question #2 : How To Find Inverse Variation

varies inversely as the square root of . If x = 15 , then A = 45 . Find if x = 30 (nearest tenth, if applicable).

Possible Answers:

31.8

63.6

22.5

11.3

Correct answer:

31.8

Explanation:

The variation equation is $A = \frac{K}{\sqrt{x}}$ for some constant of variation .

Substitute the numbers from the first scenario to find :

$45= \frac{K}{\sqrt{15}}$

$K = 45 \sqrt{15}$

The equation is now $A = \frac{45 \sqrt{15}}{\sqrt{x}}$ .

If x = 30 , then

$A = \frac{45 \sqrt{15}}{\sqrt{30}} \approx 31.8$

Report an Error

Example Question #1 : How To Find Inverse Variation

varies inversely as the square of . If x = 15 , then A = 45 . Find if x = 30 (nearest tenth, if applicable).

Possible Answers:

63.6

11.3

31.8

22.5

Correct answer:

11.3

Explanation:

The variation equation is $A = \frac{K}{x^{2}}$ for some constant of variation .

Substitute the numbers from the first scenario to find :

$45= \frac{K}{15^{2}} = \frac{K}{225}$

$K = 45 \cdot225 = 10,125$

The equation is now $A = \frac{10,125}{x^{2}}$ .

If x = 30 , then

$A = \frac{10,125}{30^{2}} = \frac{10,125}{900} \approx 11.3$

Report an Error

Example Question #2 : How To Find Inverse Variation

The current, in amperes, that a battery provides an electrical object is inversely proportional to the resistance, in ohms, of the object.

A battery provides 1.2 amperes of current to a flashlight whose resistance is measured at 20 ohms. How much current will the same battery supply to a flashlight whose resistance is measured at 16 ohms?

Possible Answers:

$0.96 \textrm{ A}$

$1.8 \textrm{ A}$

$1.6 \textrm{ A}$

$1.5 \textrm{ A}$

$2 \textrm{ A}$

Correct answer:

$1.5 \textrm{ A}$

Explanation:

If is the current and is the resistance, then we can write the variation equation for some constant of variation :

$I = \frac{k}{R}$

or, alternatively,

k=IR

To find , substitute I = 1.2,R=20 :

$k=1.2 \cdot 20 = 24$

The equation is $I = \frac{24}{R}$ . Now substitute R = 16 and solve for :

$I = \frac{24}{16} = 1.5 \textrm{ A}$

Report an Error

Example Question #7 : How To Find Inverse Variation

If is inversely proportional to and knowing that c=3 when d=5 , determine the proportionality constant.

Possible Answers:

Correct answer:

Explanation:

The general formula for inverse proportionality for this problem is

$c=\frac{k}{d}$

Given that c=3 when d=5 , we can find by plugging them into the formula.

$3=\frac{k}{5}$

Solve for by multiplying both sides by 5

$3\cdot5=\frac{k}{5}\cdot5$

15=k

So k=15 .

Report an Error

View Algebra Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Algebra Tutors

Arianna
Certified Tutor

Washington State University, Bachelor in Arts, Communication, General. City University of Seattle, Masters in Business Admini...

View Algebra Tutors

Ivory
Certified Tutor

Hopkinsville Community College, Associate, Associates in Science. Western Kentucky University, Bachelor in Arts, Psychology.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Denver, SAT Tutors in Atlanta, LSAT Tutors in Phoenix, Spanish Tutors in Chicago, Calculus Tutors in Washington DC, MCAT Tutors in San Francisco-Bay Area, Physics Tutors in Philadelphia, GRE Tutors in Chicago, Statistics Tutors in New York City, ACT Tutors in San Diego

Popular Courses & Classes

GRE Courses & Classes in Atlanta, SSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Seattle, Spanish Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in Washington DC, ACT Courses & Classes in Washington DC, MCAT Courses & Classes in Miami, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in Washington DC, ACT Test Prep in Houston, ISEE Test Prep in Boston, ACT Test Prep in Phoenix, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Miami, MCAT Test Prep in Atlanta, SAT Test Prep in Atlanta, SSAT Test Prep in Washington DC

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 1 : How to find inverse variation

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #2 : How To Find Inverse Variation

Example Question #2 : How To Find Inverse Variation

Example Question #3 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #2 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #2 : How To Find Inverse Variation

Example Question #7 : How To Find Inverse Variation

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: