Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to find f(x)

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 #3351 : Algebra 1

A function is defined by the following set of ordered pairs:

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

What is its inverse?

Possible Answers:

$\left \{ (-1,5), (-2,4), (-3,2), (-4,3), (-5,5) \right \}$

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

$\left \{ (1,-5), (2,-4), (3,-2), (4,-3), (5,-5) \right \}$

The function does not have an inverse.

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

Correct answer:

The function does not have an inverse.

Explanation:

The inverse of a function is the relation that switches the positions of the coordinates of each ordered pair. However, for a function to have an inverse, the result of those switches must itself be a function. The switches yield the relation

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

which is not a function, since the -coordinate 5 is paired with two -coordinates, 1 and 5.

Report an Error

Example Question #3352 : Algebra 1

What is the inverse of the function defined by the following set of ordered pairs?

$\left \{ (1,9), (2,8), (3,7), (4,6), (5,5) \right \}$

Possible Answers:

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$

The function does not have an inverse.

$\left \{ (1,-9), (2,-8), (3,-7), (4,-6), (5,-5) \right \}$

$\left \{ \left(1,\frac{1}{9} \right ), \left(2,\frac{1}{8} \right ), \left(3,\frac{1}{7} \right ), \left(4,\frac{1}{6} \right ), \left(5,\frac{1}{5} \right ) \right \}$

$\left \{ (-1,-9), (-2,-8), (-3,-7), (-4,-6), (-5,-5) \right \}$

Correct answer:

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$

Explanation:

The inverse of a function is the relation that switches the positions of the coordinates of each ordered pair. Therefore, the correct choice is

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$ .

Report an Error

Example Question #3353 : Algebra 1

Find the inverse of this function.

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

Possible Answers:

No inverse exists

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

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

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

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

Correct answer:

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

Explanation:

The inverse of an equation is given by solving for the x value in terms of y. To find the inverse, take the original equation, $y=\frac{x}{x-3}$ , and solve for x.

First multiply both sides by (x – 3).

y(x-3)=x

Distribute y into the parenthesis.

xy-3y=x

Subtract xy to both sides.

-3y=x-xy

Factor the x.

-3y=x(1-y)

Divide both sides by (1 – y).

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

Once you have solved for x, switch the x and y terms.

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

Though an inverse function is found by solving for x, it still must follow the "y=" convention.

Report an Error

Example Question #3354 : Algebra 1

Given $f{\left (x \right )}= x^{2} - 5, g\left ( x \right ) = 2x -3$

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

Possible Answers:

$4x^{2}-12x + 4$

2x-8

$4x^{2}-6x +5$

$x^{2}+2x -8$

$4x^{2}+4$

Correct answer:

$4x^{2}-12x + 4$

Explanation:

$f\left ( x \right ) = x^{2} -5$

Replacing or substituting g(x) for in $f\left ( x \right )$ we get $f(g\left ( x \right ))=$

$\left ( 2x-3 \right )^{2}-5$

When simplified we get

$4x^{2}-12x +4$

which is the correct answer.

Report an Error

Example Question #3355 : Algebra 1

Given $f\left ( x \right ) = x^{2}-5\ and\ g(x) = 2x-3$

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

Possible Answers:

$x^{2}+2x -8$

$2x^{2} - 13$

$2x^{2}-10$

$4x^{2}-12x+4$

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

Correct answer:

$2x^{2} - 13$

Explanation:

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

which is equal to

$2x^{2} - 13$

Report an Error

Example Question #26 : How To Find F(X)

Given $f\left ( x \right ) = x^{2} - 5$ .

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

Possible Answers:

$x^{4} - 10x^{2} + 20$

$x^{2} - 5$

$x^{2} - 10$

$\left (x^{2} - 5\right )^{2}$

$\left ( x^{2}\ - 5)^{4}$

Correct answer:

$x^{4} - 10x^{2} + 20$

Explanation:

Given $f\left ( x \right )$ = $x^{2}- 5$

Replacing in the above equation with $f\left ( x \right )$

one gets $\left ( x^{2} - 5\right )^{2} -5$

Upon simplification one gets the correct answer which is

$x^{4}-10x^{2} + 20$

Report an Error

Example Question #3361 : Algebra 1

Given $g\left ( x \right ) = 2x-5$

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

Possible Answers:

4x-15

$\left (2x-5 \right )^{2}$

$4x^{}2 + 25$

2x-5

$4x^{2} -25$

Correct answer:

4x-15

Explanation:

$g\left ( x \right ) = 2x-5$

Substituting g(x) in place of above equation one gets the following:

$2\left ( 2x-5 \right ) - 5$

which, after simplification, gives us the correct answer which is

4x-15

Report an Error

Example Question #3362 : Algebra 1

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

and $g\left ( x \right ) = 2x+3$

Find $f\left ( -2 \right ) - g\left ( -2 \right )$

Possible Answers:

Correct answer:

Explanation:

$f\left ( -2 \right ) - g\left ( -2 \right ) = \left [-\left ( -2 \right )^{2} - 3 \right ] - \left [ 2\left ( -2 \right ) +3\right ]$

=-4-3-(-4+3)

=-7-(-1)

=-7+1

=-6

Report an Error

Example Question #3363 : Algebra 1

There exists a function f(x) = 3x + 2 for x = 2, 3, 4, 5, and 6. What is the average value of the function?

Possible Answers:

Correct answer:

Explanation:

First we need to find the values of the function: f(2) = 3 * 2 + 2 = 8, f(3) = 11, f(4) = 14, f(5) = 17, and f(6) = 20. Then we can take the average of the five numbers:

average = (8 + 11 + 14 + 17 + 20) / 5 = 14

Report an Error

Example Question #1 : Function Notation

Solve the function for . When f(x)=16

What does equal when, f(x)=16

$f(x)=x^{2}-9$

Possible Answers:

-5

$\sqrt{5}$

$\pm5$

Correct answer:

$\pm5$

Explanation:

Plug 16 in for f(x) . 16=x^2-9

Add 9 to both sides. x^2=25

Take the square root of both sides. $\sqrt{25}$ = $\sqrt{x^{2}}$

Final answer is $\pm5$

Report an Error

View Algebra Tutors

Jeffrey
Certified Tutor

View Algebra Tutors

Morgan
Certified Tutor

Grand Canyon University, Bachelor of Science, Elementary School Teaching.

View Algebra Tutors

Emmanuel
Certified Tutor

Case Western Reserve University, Bachelor in Arts, Chemistry. Case Western Reserve University, Master of Science, Anatomy.

All Algebra 1 Resources

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

Popular Subjects

SAT Tutors in Los Angeles, Statistics Tutors in Washington DC, Calculus Tutors in Chicago, Spanish Tutors in Philadelphia, Physics Tutors in Denver, Physics Tutors in Dallas Fort Worth, Biology Tutors in Seattle, GMAT Tutors in San Francisco-Bay Area, Computer Science Tutors in Phoenix, Reading Tutors in Washington DC

Popular Courses & Classes

SAT Courses & Classes in Washington DC, ACT Courses & Classes in Atlanta, LSAT Courses & Classes in Boston, GRE Courses & Classes in Washington DC, ACT Courses & Classes in Miami, LSAT Courses & Classes in New York City, SAT Courses & Classes in New York City, SAT Courses & Classes in Miami, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SSAT Test Prep in Miami, ISEE Test Prep in Boston, MCAT Test Prep in Seattle, GRE Test Prep in Atlanta, SSAT Test Prep in Phoenix, GMAT Test Prep in Los Angeles, MCAT Test Prep in Philadelphia, ACT Test Prep in Dallas Fort Worth, ACT Test Prep in Seattle, GRE 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

Algebra 1 : How to find f(x)

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #3351 : Algebra 1

Example Question #3352 : Algebra 1

Example Question #3353 : Algebra 1

Example Question #3354 : Algebra 1

Example Question #3355 : Algebra 1

Example Question #26 : How To Find F(X)

Example Question #3361 : Algebra 1

Example Question #3362 : Algebra 1

Example Question #3363 : Algebra 1

Example Question #1 : Function Notation

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: