We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : How to find domain and range of the inverse of a relation

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find Domain And Range Of The Inverse Of A Relation

What is the range of the function y = x² + 2?

Possible Answers:

{2}

y ≥ 2

{–2, 2}

all real numbers

undefined

Correct answer:

y ≥ 2

Explanation:

The range of a function is the set of y-values that a function can take. First let's find the domain. The domain is the set of x-values that the function can take. Here the domain is all real numbers because no x-value will make this function undefined. (Dividing by 0 is an example of an operation that would make the function undefined.)

So if any value of x can be plugged into y = x² + 2, can y take any value also? Not quite! The smallest value that y can ever be is 2. No matter what value of x is plugged in, y = x² + 2 will never produce a number less than 2. Therefore the range is y ≥ 2.

Report an Error

Example Question #2 : How To Find Domain And Range Of The Inverse Of A Relation

Which of the following values of x is not in the domain of the function y = (2x – 1) / (x² – 6x + 9) ?

Possible Answers:

1/2

–1/2

Correct answer:

Explanation:

Values of x that make the denominator equal zero are not included in the domain. The denominator can be simplified to (x – 3)², so the value that makes it zero is 3.

Report an Error

Example Question #1 : How To Find Domain And Range Of The Inverse Of A Relation

Given the relation below:

{(1, 2), (3, 4), (5, 6), (7, 8)}

Find the range of the inverse of the relation.

Possible Answers:

{2, 4, 6, 8}

{1, 2, 3, 4}

{1, 3, 5, 7}

{5, 6, 7, 8}

the inverse of the relation does not exist

Correct answer: {1, 3, 5, 7}

Explanation:

The domain of a relation is the same as the range of the inverse of the relation. In other words, the x-values of the relation are the y-values of the inverse.

Report an Error

Example Question #4 : How To Find Domain And Range Of The Inverse Of A Relation

What is the range of the function y = x² + 2?

Possible Answers:

{2}

all real numbers

y ≥ 2

{–2, 2}

undefined

Correct answer:

y ≥ 2

Explanation:

Report an Error

Example Question #5 : How To Find Domain And Range Of The Inverse Of A Relation

What is the smallest value that belongs to the range of the function $f(x)=2|4-x|-2$ ?

Possible Answers:

$\dpi{100} -2$

$\dpi{100} 4$

$\dpi{100} 0$

$\dpi{100} 2$

$\dpi{100} -4$

Correct answer:

$\dpi{100} -2$

Explanation:

We need to be careful here not to confuse the domain and range of a function. The problem specifically concerns the range of the function, which is the set of possible numbers of $\dpi{100} f(x)$ . It can be helpful to think of the range as all the possible y-values we could have on the points on the graph of $\dpi{100} f(x)$ .

Notice that $\dpi{100} f(x)$ has $\dpi{100} |4-x|$ in its equation. Whenever we have an absolute value of some quantity, the result will always be equal to or greater than zero. In other words, |4-x| $\geq$ 0. We are asked to find the smallest value in the range of $\dpi{100} f(x)$ , so let's consider the smallest value of $\dpi{100} |4-x|$ , which would have to be zero. Let's see what would happen to $\dpi{100} f(x)$ if $\dpi{100} |4-x|=0$ .

$\dpi{100} f(x)=2(0)-2=0-2=-2$

This means that when $\dpi{100} |4-x|=0$ , $\dpi{100} f(x)=-2$ . Let's see what happens when $\dpi{100} |4-x|$ gets larger. For example, let's let $\dpi{100} |4-x|=3$ .

$\dpi{100} f(x)=2(3)-2=4$

As we can see, as $\dpi{100} |4-x|$ gets larger, so does $\dpi{100} f(x)$ . We want $\dpi{100} f(x)$ to be as small as possible, so we are going to want $\dpi{100} |4-x|$ to be equal to zero. And, as we already determiend, $\dpi{100} f(x)$ equals $\dpi{100} -2$ when $\dpi{100} |4-x|=0$ .

The answer is $\dpi{100} -2$ .

Report an Error

Example Question #2 : How To Find Domain And Range Of The Inverse Of A Relation

If $f(x) = x - 3$ , then find $f^{-1}(x)$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

$f(x) = x - 3$ is the same as $y= x - 3$ .

To find the inverse simply exchange $x$ and $y$ and solve for $y$ .

So we get $x=y-3$ which leads to $y=x+3$ .

Report an Error

Example Question #1 : How To Find Domain And Range Of The Inverse Of A Relation

If $f(x)=\frac{x}{x-3}$ , then which of the following is equal to $f^{-1}(x)$ ?

Possible Answers:

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

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

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

$\frac{-3x}{x+1}$

Correct answer:

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

Explanation:

Inversef2

Inverse3

Report an Error

Example Question #2 : How To Find Domain And Range Of The Inverse Of A Relation

Given the relation below, identify the domain of the inverse of the relation.

$\left \{(1, 2), (3, 4), (5, 6), (7, 8){ \right \}$

Possible Answers:

The inverse of the relation does not exist.

$\left \{ 5,\ 6,\ 7,\ 8 \right \}$

$\left \{ 1,\ 2,\ 3,\ 4 \right \}$

$\left \{ 1,\ 3,\ 5,\ 7 \right \}$

$\left \{ 2,\ 4,\ 6,\ 8 \right \}$

Correct answer:

$\left \{ 2,\ 4,\ 6,\ 8 \right \}$

Explanation:

$\left \{(1, 2), (3, 4), (5, 6), (7, 8){ \right \}$

The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.

For the original relation, the range is: $\left \{ 2,\ 4,\ 6,\ 8 \right \}$ .

Thus, the domain for the inverse relation will also be $\left \{ 2,\ 4,\ 6,\ 8 \right \}$ .

Report an Error

View PSAT Mathematics Tutors

Ayan
Certified Tutor

Vellore Institute of Technology, Bachelor, Chemical Engineering. University of Calgary, Master's/Graduate, Chemical and Petro...

View PSAT Mathematics Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

View PSAT Mathematics Tutors

Shakeel
Certified Tutor

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Philadelphia, French Tutors in San Francisco-Bay Area, Statistics Tutors in Dallas Fort Worth, Physics Tutors in Houston, ACT Tutors in Chicago, GRE Tutors in San Francisco-Bay Area, Computer Science Tutors in Washington DC, Spanish Tutors in Miami, LSAT Tutors in Denver, Algebra Tutors in Philadelphia

Popular Courses & Classes

ISEE Courses & Classes in Los Angeles, LSAT Courses & Classes in Denver, GRE Courses & Classes in Denver, GMAT Courses & Classes in San Diego, SSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in New York City, GRE Courses & Classes in Houston, SAT Courses & Classes in Phoenix, ISEE Courses & Classes in Boston, SSAT Courses & Classes in Chicago

Popular Test Prep

ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Los Angeles, GRE Test Prep in Los Angeles, LSAT Test Prep in Atlanta, MCAT Test Prep in Washington DC, ISEE Test Prep in Philadelphia, GRE Test Prep in New York City, ACT Test Prep in Boston, ACT 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

PSAT Math : How to find domain and range of the inverse of a relation

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Find Domain And Range Of The Inverse Of A Relation

Example Question #2 : How To Find Domain And Range Of The Inverse Of A Relation

Example Question #1 : How To Find Domain And Range Of The Inverse Of A Relation

Example Question #4 : How To Find Domain And Range Of The Inverse Of A Relation

Example Question #5 : How To Find Domain And Range Of The Inverse Of A Relation

Example Question #2 : How To Find Domain And Range Of The Inverse Of A Relation

Example Question #1 : How To Find Domain And Range Of The Inverse Of A Relation

Example Question #2 : How To Find Domain And Range Of The Inverse Of A Relation

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: