Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Pre-Calculus

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 #171 : Functions

f(x)=x^2-3 and g(x)=2x+3 . Find $(f\circ g)(x)$ .

Possible Answers:

$(f\circ g)(x)=2x^2+12x+12$

$(f\circ g)(x)=4x^2+12x+6$

$(f\circ g)(x)=2x^2-6$

$(f\circ g)(x)=4x^2-12x+9$

$(f\circ g)(x)=2x^2-3$

Correct answer:

$(f\circ g)(x)=4x^2+12x+6$

Explanation:

${\color{Blue} f(x)=x^2-3}$ and ${\color{Red} g(x)=2x+3}$ .

To find $(f\circ g)(x)$ we plug in the function g(x) everywhere there is a variable in the function f(x) .

This is the composition of "f of g of x".

$(f\circ g)(x)=f(g(x))={\color{Blue} (}{\color{Red} 2x+3}{\color{Blue} )}{\color{Blue} ^2-3}$

Foil the square and simplify:

$(f\circ g)(x)=(4x^2+12x+9)=\mathbf{4x^2+12x+6}$

Report an Error

Example Question #21 : Composition Of Functions

If f(x)=3x+1 and g(x) = x^3 , what must g(f(-1))+1 be?

Possible Answers:

Correct answer:

Explanation:

Evaluate the composite function g(f(-1)) first.

Solve for f(-1) by substituting into the value for f(x) .

f(-1)=3(-1)+1 = -3+1 = -2

The value of f(-1) will be replaced inside g(f(-1)) , which will become g(-2) .

Evaluate g(-2) .

g(-2) = (-2)^3= (-2)(-2)(-2) = -8

The value of g(f(-1)) is . Add one to this value.

-8+1 = -7

The answer is .

Report an Error

Example Question #21 : Composition Of Functions

Find f(g(2)) given

f(x)=2x+3 and g(x)=3x-7

Possible Answers:

Correct answer:

Explanation:

To evaluate, first evaluate g(2) and then plug in that answer into f(x) . Thus,

g(2)=3(2)-7=-1

Then, f(-1) is

f(-1)=2(-1)+3=1

Report an Error

Example Question #1131 : Pre Calculus

Find f(g(1)) given the following.

f(x)=2x+3

g(x)=3x-4

Possible Answers:

Correct answer:

Explanation:

To solve, plug 1 into g and then your answer into f.

Thus,

g(1)=3(1)-4=-1

Plugging in this value into our f function we get the final answer as follows.

f(-1)=2(-1)+3=1

Report an Error

Example Question #1132 : Pre Calculus

Find g(f(2)) given the following functions:

f(x)=x-6

g(x)=-3x-10

Possible Answers:

Correct answer:

Explanation:

To solve, simply plug in 2 into f and then the result into g.

Thus,

f(2)=2-6=-4

g(-4)=(-3)*(-4)-10=12-10=2

Report an Error

Example Question #1133 : Pre Calculus

Suppose f(x)=3x^2 and g(x)=x+1 . Find f(g(x)) .

Possible Answers:

f(g(x))=3x^2+3

f(g(x))=3x^2+2x+1

f(g(x))=3x^2+1

f(g(x))=3x^2

f(g(x))=3x^2+6x+3

Correct answer:

f(g(x))=3x^2+6x+3

Explanation:

To find f(g(x)) , you must subsititue g(x) into the function, .

f(g(x))=3(g(x))^2

f(g(x))=3(x+1)^2

f(g(x))=3(x^2+2x+1)

f(g(x))=3x^2+6x+3

Report an Error

Example Question #23 : Composition Of Functions

If f(x) = x^2 and g(x) = 3x+3 , what is f(g(3))?

Possible Answers:

144

Correct answer:

144

Explanation:

First, we find g(3), or 3(3)+3 =12. Then, find f(12) , or 12^2 = 144.

Report an Error

Example Question #182 : Functions

Given f(x)=x^2-2x and g(x)=x+2 find f(g(x)) .

Possible Answers:

f(g(x))=x^2+2x+4

f(g(x))=x^2+4x

f(g(x))=x^2+2x

None of these.

f(g(x))=x^2+4x+2

Correct answer:

f(g(x))=x^2+2x

Explanation:

Finding f(g(x)) is the same as plugging in g(x) into f(x) much like one would find f(2){} for a function f(x) .

f(x)=x^2-2x and g(x)=x+2

Insert g(x) into f(x) everywhere there is a variable in f(x):

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

Report an Error

Example Question #1139 : Pre Calculus

We are given the following:

$f(x)=x^2+3\hspace{5mm}$ and g(x)=x+3 .

Find:

$(f\circ g)(x)$

Possible Answers:

$(f\cdot g)(x)=x^2+6x+9$

$(f\cdot g)(x)=2x^2+6x+12$

None of the other answers.

$(f\cdot g)(x)=x^2+3x+6$

$(f\cdot g)(x)=x^2+9x+12$

Correct answer:

None of the other answers.

Explanation:

Let's discuss what the problem is asking us to solve. The expression $(f\cdot g)(x)$ (read as as "f of g of x") is the same as f(g(x)) . In other words, we need to substitute g(x) into f(x) .

Substitute the equation of g(x) for the variable in the given f(x) function:

$(f\cdot g)(x)=(x+3)^{ 2} {+3}$

Next we need to FOIL the squared term and simplify:

(x+3)^2=(x+3)(x+3)

FOIL means that we multiply terms in the following order: first, outer, inner, and last.

First: $x\cdot x=x^2$

Outer: $x\cdot 3=3x$

Inner: $3\cdot x=3x$

Last: $3\cdot 3=9$

When we combine like terms, we get the following:

x^2+6x+9

Substitute this back into the equation and continue to simplify.

$(f\cdot g)(x)=x^2+6x+9+3$

$(f\cdot g)(x)=x^2+6x+12$

None of the answers are correct.

Report an Error

Example Question #1131 : Pre Calculus

Simplify

$\frac{9^{\frac{2}{3}}\cdot 3^{\frac{5}{3}}}{6^{2}}$

Possible Answers:

$\frac{9}{2}$

$\frac{3}{4}$

$\frac{9}{4}$

$\frac{27}{2}$

Correct answer:

$\frac{3}{4}$

Explanation:

$\frac{9^{\frac{2}{3}}\cdot 3^{\frac{5}{3}}}{6^{2}}=\frac{(3^{2})^{\frac{2}{3}}\cdot3^{\frac{5}{3}}}{6^{2}}=\frac{3^{\frac{4}{3}}\cdot 3^{\frac{5}{3}}}{6^{2}}$

$=\frac{3^\frac{9}{3}}{6^2}=\frac{3^3}{6^2}=\frac{27}{36}=\frac{3}{4}$ .

Report an Error

View Pre-Calculus Tutors

Rodolfo
Certified Tutor

The University of Texas at San Antonio, Bachelor of Science, Mathematics.

View Pre-Calculus Tutors

Carolyn
Certified Tutor

University of Miami, Bachelor of Science, Biology, General. University of Alaska Fairbanks, Master of Science, Fishing and Fi...

View Pre-Calculus Tutors

Sharon
Certified Tutor

American InterContinental University - London, Masters in Education, Education.

All Precalculus Resources

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

Popular Subjects

ACT Tutors in Seattle, Spanish Tutors in Philadelphia, French Tutors in Denver, LSAT Tutors in Boston, English Tutors in Seattle, LSAT Tutors in Miami, Algebra Tutors in Atlanta, Statistics Tutors in Chicago, Biology Tutors in San Francisco-Bay Area, Statistics Tutors in Philadelphia

Popular Courses & Classes

Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in Boston, MCAT Courses & Classes in Los Angeles, ACT Courses & Classes in Phoenix, Spanish Courses & Classes in Houston, GMAT Courses & Classes in Denver, ACT Courses & Classes in Miami, Spanish Courses & Classes in New York City, GRE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Seattle, LSAT Test Prep in Miami, SAT Test Prep in Boston, SSAT Test Prep in Miami, GRE Test Prep in Chicago, SSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Chicago, ACT Test Prep in Phoenix, SAT Test Prep in Chicago, ISEE Test Prep in Houston

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 : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #171 : Functions

Example Question #21 : Composition Of Functions

Example Question #21 : Composition Of Functions

Example Question #1131 : Pre Calculus

Example Question #1132 : Pre Calculus

Example Question #1133 : Pre Calculus

Example Question #23 : Composition Of Functions

Example Question #182 : Functions

Example Question #1139 : Pre Calculus

Example Question #1131 : Pre Calculus

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: