We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #27 : Function Notation

Given f(x) = 3x+3 and g(x)=-3 , what is g(f(x))+2g(x) ?

Possible Answers:

$\textup{The answer cannot be determined.}$

Correct answer:

Explanation:

Evaluate g(f(x)) first. If we plugged in the function f(x) = 3x+3 into the function g(x)=-3 , no matter what is replaced with, the final output will always be negative three.

g(3x+3)= -3

Evaluate 2g(x) . Multiply the function g(x)=-3 by two.

2g(x) = -6

Sum both numbers.

-3+(-6) = -3-6=-9

The answer is:

Report an Error

Example Question #24 : Function Notation

If g(x)=1 , f(x)=2 , and $h(x)= \pi$ , what is 2f(g(x))+h(g(x)) ?

Possible Answers:

$\pi+1$

$\pi +4$

$2\pi+2$

$2\pi+4$

$\pi+2$

Correct answer:

$\pi +4$

Explanation:

Evaluate each term separately.

The term f(g(x)) means to input the function g(x)=1 into the function f(x) .

$2f(g(x)) = 2\cdot f(1) = 2\cdot 2 = 4$

Follow suit for h(g(x)) . Substitute g(x)=1 into the function h(x) .

$h(g(x)) =h(1)=\pi$

Add the two known terms.

$2f(g(x))+h(g(x)) = 4+\pi$

The answer is: $\pi +4$

Report an Error

Example Question #25 : Function Notation

If g(x)=3x+5 , what is g(x+3) ?

Possible Answers:

3x+11

3x+55

3x+14

3x+8

3x+5

Correct answer:

3x+14

Explanation:

In order to solve g(x+3) , replace the entire quantity of (x+3) as a replacement of .

Replace the term.

g(x+3)=3(x+3)+5

Distribute the binomial.

3x+9+5 = 3x+14

The answer is: 3x+14

Report an Error

Example Question #682 : Algebra Ii

If h(x) = 2x^3 , what is h(h(2x^3)) ?

Possible Answers:

$8192x^{27}$

2x^3

4x^6

4x^9

$\textup{The answer is not given.}$

Correct answer:

$8192x^{27}$

Explanation:

Evaluate h(2x^3) first. Substitute 2x^3 into the function as a replacement of the x-variable.

h(2x^3) = 2(2x^3)^3 = 2(8x^9) = 16x^9

Substitute this value to determine h(h(2x^3)) .

h(h(2x^3)) = h(16x^9) = 2(16x^9)^3=2(16x^9)(16x^9)(16x^9)

The answer is: $8192x^{27}$

Report an Error

Example Question #31 : Function Notation

Given the function g(x)= 2x^3-6x , what is the value of g(-3) ?

Possible Answers:

Correct answer:

Explanation:

Substitute negative three into the function.

g(-3)= 2(-3)^3-6(-3)

Simplify this equation by order of operations.

2(-3)^3-6(-3) = 2(-27)+18 = -54+18

The answer is:

Report an Error

Example Question #161 : Introduction To Functions

If f(x) = 6x+6 , find $f^{-1}(6)$ .

Possible Answers:

$\frac{1}{6}$

$-\frac{1}{6}$

Correct answer:

Explanation:

To solve this question, first convert the given function to its inverse.

Rewrite f(x) = 6x+6 by replacing f(x) with .

y= 6x+6

Interchange the x and y variables.

x=6y+6

Solve for y. Subtract 6 from both sides.

x-6=6y+6-6

Simplify, and divide by 6 on both sides.

$\frac{x-6}{6}=\frac{6y}{6}$

Simplify both sides.

The inverse function is: $y= f^{-1}(x)= \frac{1}{6}x-1$

Solve for $f^{-1}(6)$ by plugging 6 into the inverse function.

$\frac{1}{6}(6)-1 = 1-1=0$

The answer is:

Report an Error

Example Question #161 : Introduction To Functions

Given the following function, determine f(2x) if: f(x) = 3x+9

Possible Answers:

6x+9

6x+18

6x^2+9

5x+9

6x^2+18x

Correct answer:

6x+9

Explanation:

Input (2x) as the replacement of the x-variable for the function f(x) .

The equation becomes:

f(2x) = 3(2x)+9

Simplify by distribution.

The answer is: 6x+9

Report an Error

Example Question #162 : Introduction To Functions

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

Possible Answers:

$-\frac{1}{3}$

$-\frac{2}{3}$

$\frac{1}{3}$

$\frac{2}{3}$

Correct answer:

Explanation:

Replace the f(x) with .

y= 3x+3

Interchange the x and y variables.

x= 3y+3

Subtract three from both sides.

x-3= 3y+3-3

x-3= 3y

Divide by three on both sides.

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

The inverse function is: $y=\frac{1}{3}x-1$

Substitute $f^{-1}(3)$ as a replacement of .

$y=\frac{1}{3}(3)-1 = 1-1 = 0$

The answer is:

Report an Error

Example Question #36 : Function Notation

Given the function f(x)= 5x-5 , what is: $f(-\frac{1}{5})$ ?

Possible Answers:

$-\frac{9}{2}$

$-\frac{11}{2}$

$-\frac{26}{5}$

Correct answer:

Explanation:

Replace x with negative one-fifth.

$f(-\frac{1}{5})= 5(-\frac{1}{5})-5$

Simplify the expression. When a number is subtracted from a

-1-5 = -6

The answer is .

Report an Error

Example Question #681 : Algebra Ii

Evaluate $g(f(\frac{1}{95}))$ if: g(x) = 95 and $f(x) = \frac{1}{95}$

Possible Answers:

$\frac{1}{9025}$

9025

$\frac{1}{95}$

Correct answer:

Explanation:

Evaluate $g(f(\frac{1}{95}))$ by solving for $f(\frac{1}{95})$ first.

No matter what value of , $f(x) = \frac{1}{95}$ . This means that:

$f( \frac{1}{95}) = \frac{1}{95}$

Then:

$g(\frac{1}{95})$

For any value of , g(x) = 95 . This means that:

$g(\frac{1}{95}) = 95$

The answer is:

Report an Error

View Algebra 2 Tutors

Christopher
Certified Tutor

Kean University, Bachelors, Mathematics. Concordia University-Portland, Masters, Educational Leadership.

View Algebra 2 Tutors

Jessica
Certified Tutor

Nevada State College, Bachelor of Science, High School Teaching.

View Algebra 2 Tutors

Divyansh
Certified Tutor

Dalhousie University, Bachelor of Technology, Chemical Engineering.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Denver, English Tutors in Washington DC, SSAT Tutors in Phoenix, English Tutors in Boston, GMAT Tutors in Atlanta, Calculus Tutors in Atlanta, Statistics Tutors in Philadelphia, ISEE Tutors in Houston, GMAT Tutors in San Francisco-Bay Area, French Tutors in Miami

Popular Courses & Classes

ISEE Courses & Classes in Houston, Spanish Courses & Classes in New York City, MCAT Courses & Classes in San Diego, GMAT Courses & Classes in Philadelphia, SSAT Courses & Classes in New York City, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Phoenix, SAT Courses & Classes in Denver, GMAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Atlanta, SAT Test Prep in Denver, SSAT Test Prep in Boston, ACT Test Prep in Dallas Fort Worth, MCAT Test Prep in Washington DC, ACT Test Prep in Atlanta, SAT Test Prep in Phoenix, GMAT Test Prep in Boston, MCAT 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

Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #27 : Function Notation

Example Question #24 : Function Notation

Example Question #25 : Function Notation

Example Question #682 : Algebra Ii

Example Question #31 : Function Notation

Example Question #161 : Introduction To Functions

Example Question #161 : Introduction To Functions

Example Question #162 : Introduction To Functions

Example Question #36 : Function Notation

Example Question #681 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: