Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Composition of Functions

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 #1 : Composition Of Functions

Suppose f(x) = 9 - x^3 and g(x) = ln (x+1)

What would g(f(x)) be?

Possible Answers:

9 - ln^2(x+1)

ln (9-x^3)

ln (10 - x^3)

10 - ln^3(x + 1)

ln(10 + x - x^3)

Correct answer:

ln (10 - x^3)

Explanation:

Substitute f(x) = 9 -x^3 into the function g(x) = ln (x+1) for .

Then it will become:

g(9 - x^3) = ln ((9-x^3) + 1) = ln (10 - x^3)

Report an Error

Example Question #2 : Composition Of Functions

$f(x)=3-2x^2+\ln(x)$

g(x)=e^x

What is f(g(x)) ?

Possible Answers:

$3-2e^{2x} +x$

2x^2 +x

3-2e^x +x

3-2x^2+e^x

$3-2e^{2x} +\ln(2e^x)$

Correct answer:

$3-2e^{2x} +x$

Explanation:

f(g(x)) simply means: where ever you see an x in the equation f(x), replace it with g(x).

So, doing just that, we get

$3-2(e^x)^2+\ln(e^x)$ ,

which simplifies to

$3-2e^{2x}+x\ln(e)$ .

Since

$\ln(e)=1$ our simplified expression becomes,

$3-2e^{2x} +x$ .

Report an Error

Example Question #2 : Composition Of Functions

f(x)=2-5x

$g(x)=\frac{3x^2}{x}-6$

What is g(f(x)) ?

Possible Answers:

-15x

225x^2 +6

12-15x

$\frac{75x}{4}$

-15x+32

Correct answer:

-15x

Explanation:

g(f(x)) simply means replacing every x in g(x) with f(x).

$\frac{3(2-5x)^2}{(2-5x)}-6$

After simplifying, it becomes

$\frac{3(2-5x)(2-5x)}{(2-5x)}-6$

=3(2-5x)-6

=6-15x-6=-15x

Report an Error

Example Question #3 : Composition Of Functions

For the functions

f(x)=4x

and

g(x)=x^2 .

Evaluate the composite function

$f\circ g$ .

Possible Answers:

DNE

4x^2

8x^3

16x^2

Correct answer:

4x^2

Explanation:

The composite function means to plug in the function of g(x) into the function f(x) for every x value in the function.

Therefore the composition function becomes:

$f\circ g = f[g(x)] = 4(x^2) = 4x^2$ .

Report an Error

Example Question #4 : Composition Of Functions

For the functions

f(x)=x+4

and

g(x)=x^2 .

Evaluate the composite function

$f\circ g$ .

Possible Answers:

x^2+4

DNE

x^2+x+4

x^2+8x+16

Correct answer:

x^2+4

Explanation:

The composite function means to plug in the function g(x) into f(x) for every x value.

Therefore the composite function becomes,

$f\circ g = f[g(x)] = (x^2)+4 = x^2+4$

Report an Error

Example Question #4 : Composition Of Functions

If f(x)=x^2-3 , g(x)=6x+4 , and h(x)=x+8 , what is f(g(h(-7))) ?

Possible Answers:

288

Correct answer:

Explanation:

When doing a composition of functions such as this one, you must always remember to start with the innermost parentheses and work backward towards the outside.

So, to begin, we have

h(-7)=(-7)+8=1 .

Now we move outward, getting

g(h(-7))=g(1)=6(1)+4=10 .

Finally, we move outward one more time, getting

f(g(h(-7)))=f(g(1))=f(10)=(10)^2-3=97 .

Report an Error

Example Question #3 : Composition Of Functions

Find g(h(i(2))) if g(x) = x , h(x) = 3 , and i(x)=x^4 .

Possible Answers:

3+x

48x

Correct answer:

Explanation:

Solve for the value of i(2) .

i(2)= 2^4=16

Solve for the value of h(i(2)) .

h(i(2))=h(16) = 3

Solve for the value g(h(i(2))) .

g(h(i(2)))=g(3) = 3

Report an Error

Example Question #8 : Composition Of Functions

For the functions f(x)=x+7 and $g(x)=x^{3}$ , evaluate the composite function $f\circ g$

Possible Answers:

$(x+7)^{3}$

$x^{3}+7x^{2}+14x+21$

$x^{3}+21x^{2}$

$x^{3}+49x^{2}$

$x^{3}+7$

Correct answer:

$x^{3}+7$

Explanation:

The composite function notation $f\circ g$ means to swap the function g(x) into f(x) for every value of . Therefore:

$f\circ g$

=f[g(x)]

$=(x^{3})+7$

$=x^{3}+7$

Report an Error

Example Question #5 : Composition Of Functions

For the functions f(x)=x-7 and g(x)=4x+6 , evaluate the composite function $g\circ f$ .

Possible Answers:

3x+13

3x-1

4x-22

4x-1

4x-13

Correct answer:

4x-22

Explanation:

The composite function notation $g\circ f$ means to swap the function f(x) into g(x) for every value of . Therefore:

$g\circ f$

=g[f(x)]

=4(x-7)+6

=4x-28+6

=4x-22

Report an Error

Example Question #10 : Composition Of Functions

For the functions $f(x)=x^{2}-4$ and g(x)=2x+3 , evaluate the composite function $f\circ g$ .

Possible Answers:

$4x^{2}+12x+5$

$2x^{2}-4$

$4x^{2}+12x+9$

None of the answers listed

$2x^{2}-1$

Correct answer:

$4x^{2}+12x+5$

Explanation:

The composite function notation $f\circ g$ means to swap the function g(x) into f(x) for every value of . Therefore:

$f\circ g$

=f[g(x)]

$=(2x+3)^{2}-4$

$=4x^{2}+12x+9-4$

$=4x^{2}+12x+5$

Report an Error

View Pre-Calculus Tutors

Jonathan
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Mathematics.

View Pre-Calculus Tutors

Sydney
Certified Tutor

University of Vermont, Bachelor of Science, Nursing (RN). University of Connecticut, Bachelor of Science, Health Sciences, Ge...

View Pre-Calculus Tutors

James
Certified Tutor

St. Mary of the Plains College, Bachelors, Mathematics. Baker University, Masters, Business Administration and Management.

All Precalculus Resources

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

Popular Subjects

English Tutors in Miami, Math Tutors in Chicago, Computer Science Tutors in Houston, Spanish Tutors in Phoenix, GRE Tutors in New York City, English Tutors in Chicago, MCAT Tutors in Philadelphia, Math Tutors in Atlanta, SSAT Tutors in Phoenix, French Tutors in San Diego

Popular Courses & Classes

LSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in San Diego, ISEE Courses & Classes in San Diego, GRE Courses & Classes in Atlanta, SSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Chicago, GRE Courses & Classes in Seattle, MCAT Courses & Classes in Los Angeles

Popular Test Prep

ACT Test Prep in Chicago, MCAT Test Prep in Houston, MCAT Test Prep in Los Angeles, GRE Test Prep in Seattle, SSAT Test Prep in Denver, SAT Test Prep in Washington DC, ACT Test Prep in New York City, SSAT Test Prep in Atlanta, ISEE Test Prep in Dallas Fort Worth, SAT 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

Precalculus : Composition of Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Composition Of Functions

Example Question #2 : Composition Of Functions

Example Question #2 : Composition Of Functions

Example Question #3 : Composition Of Functions

Example Question #4 : Composition Of Functions

Example Question #4 : Composition Of Functions

Example Question #3 : Composition Of Functions

Example Question #8 : Composition Of Functions

Example Question #5 : Composition Of Functions

Example Question #10 : Composition Of Functions

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: