<< Chapter < Page Chapter >> Page >

What is the composition of two functions, f g ?

Got questions? Get instant answers now!

If the order is reversed when composing two functions, can the result ever be the same as the answer in the original order of the composition? If yes, give an example. If no, explain why not.

Yes. Sample answer: Let f ( x ) = x + 1  and  g ( x ) = x 1. Then f ( g ( x ) ) = f ( x 1 ) = ( x 1 ) + 1 = x and g ( f ( x ) ) = g ( x + 1 ) = ( x + 1 ) 1 = x . So f g = g f .

Got questions? Get instant answers now!

How do you find the domain for the composition of two functions, f g ?

Got questions? Get instant answers now!

Algebraic

For the following exercises, determine the domain for each function in interval notation.

Given f ( x ) = x 2 + 2 x   and   g ( x ) = 6 x 2 , find f + g , f g , f g ,   and   f g .

( f + g ) ( x ) = 2 x + 6 , domain: ( , )

( f g ) ( x ) = 2 x 2 + 2 x 6 , domain: ( , )

( f g ) ( x ) = x 4 2 x 3 + 6 x 2 + 12 x , domain: ( , )

( f g ) ( x ) = x 2 + 2 x 6 x 2 , domain: ( , 6 ) ( 6 , 6 ) ( 6 , )

Got questions? Get instant answers now!

Given f ( x ) = 3 x 2 + x   and   g ( x ) = 5 , find f + g , f g , f g , and   f g .

Got questions? Get instant answers now!

Given f ( x ) = 2 x 2 + 4 x   and   g ( x ) = 1 2 x , find f + g , f g , f g ,   and   f g .

( f + g ) ( x ) = 4 x 3 + 8 x 2 + 1 2 x , domain: ( , 0 ) ( 0 , )

( f g ) ( x ) = 4 x 3 + 8 x 2 1 2 x , domain: ( , 0 ) ( 0 , )

( f g ) ( x ) = x + 2 , domain: ( , 0 ) ( 0 , )

( f g ) ( x ) = 4 x 3 + 8 x 2 , domain: ( , 0 ) ( 0 , )

Got questions? Get instant answers now!

Given f ( x ) = 1 x 4 and g ( x ) = 1 6 x , find f + g , f g , f g ,   and   f g .

Got questions? Get instant answers now!

Given f ( x ) = 3 x 2 and g ( x ) = x 5 , find f + g , f g , f g ,   and   f g .

( f + g ) ( x ) = 3 x 2 + x 5 , domain: [ 5 , )

( f g ) ( x ) = 3 x 2 x 5 , domain: [ 5 , )

( f g ) ( x ) = 3 x 2 x 5 , domain: [ 5 , )

( f g ) ( x ) = 3 x 2 x 5 , domain: ( 5 , )

Got questions? Get instant answers now!

Given f ( x ) = x and g ( x ) = | x 3 | , find g f .

Got questions? Get instant answers now!

For the following exercise, find the indicated function given f ( x ) = 2 x 2 + 1 and g ( x ) = 3 x 5 .

  1. f ( g ( 2 ) )
  2. f ( g ( x ) )
  3. g ( f ( x ) )
  4. ( g g ) ( x )
  5. ( f f ) ( 2 )

a. 3; b. f ( g ( x ) ) = 2 ( 3 x 5 ) 2 + 1 ; c. f ( g ( x ) ) = 6 x 2 2 ; d. ( g g ) ( x ) = 3 ( 3 x 5 ) 5 = 9 x 20 ; e. ( f f ) ( 2 ) = 163

Got questions? Get instant answers now!

For the following exercises, use each pair of functions to find f ( g ( x ) ) and g ( f ( x ) ) . Simplify your answers.

f ( x ) = x 2 + 1 , g ( x ) = x + 2

Got questions? Get instant answers now!

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

f ( g ( x ) ) = x 2 + 3 + 2 , g ( f ( x ) ) = x + 4 x + 7

Got questions? Get instant answers now!

f ( x ) = | x | , g ( x ) = 5 x + 1

Got questions? Get instant answers now!

f ( x ) = x 3 , g ( x ) = x + 1 x 3

f ( g ( x ) ) = x + 1 x 3 3 = x + 1 3 x , g ( f ( x ) ) = x 3 + 1 x

Got questions? Get instant answers now!

f ( x ) = 1 x 6 , g ( x ) = 7 x + 6

Got questions? Get instant answers now!

f ( x ) = 1 x 4 , g ( x ) = 2 x + 4

( f g ) ( x ) = 1 2 x + 4 4 = x 2 ,   ( g f ) ( x ) = 2 x 4

Got questions? Get instant answers now!

For the following exercises, use each set of functions to find f ( g ( h ( x ) ) ) . Simplify your answers.

f ( x ) = x 4 + 6 , g ( x ) = x 6 , and h ( x ) = x

Got questions? Get instant answers now!

f ( x ) = x 2 + 1 , g ( x ) = 1 x , and h ( x ) = x + 3

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

Got questions? Get instant answers now!

Given f ( x ) = 1 x and g ( x ) = x 3 , find the following:

  1. ( f g ) ( x )
  2. the domain of ( f g ) ( x ) in interval notation
  3. ( g f ) ( x )
  4. the domain of ( g f ) ( x )
  5. ( f g ) x
Got questions? Get instant answers now!

Given f ( x ) = 2 4 x and g ( x ) = 3 x , find the following:

  1. ( g f ) ( x )
  2. the domain of ( g f ) ( x ) in interval notation

a. ( g f ) ( x ) = 3 2 4 x ; b. ( , 1 2 )

Got questions? Get instant answers now!

Given the functions f ( x ) = 1 x x and g ( x ) = 1 1 + x 2 , find the following:

  1. ( g f ) ( x )
  2. ( g f ) ( 2 )
Got questions? Get instant answers now!

Given functions p ( x ) = 1 x and m ( x ) = x 2 4 , state the domain of each of the following functions using interval notation:

  1. p ( x ) m ( x )
  2. p ( m ( x ) )
  3. m ( p ( x ) )

a. ( 0 , 2 ) ( 2 , ) ; b. ( , 2 ) ( 2 , ) ; c. ( 0 , )

Got questions? Get instant answers now!

Given functions q ( x ) = 1 x and h ( x ) = x 2 9 , state the domain of each of the following functions using interval notation.

  1. q ( x ) h ( x )
  2. q ( h ( x ) )
  3. h ( q ( x ) )
Got questions? Get instant answers now!

For f ( x ) = 1 x and g ( x ) = x 1 , write the domain of ( f g ) ( x ) in interval notation.

( 1 , )

Got questions? Get instant answers now!

For the following exercises, find functions f ( x ) and g ( x ) so the given function can be expressed as h ( x ) = f ( g ( x ) ) .

h ( x ) = ( x 5 ) 3

sample: f ( x ) = x 3 g ( x ) = x 5

Got questions? Get instant answers now!

h ( x ) = 4 ( x + 2 ) 2

sample: f ( x ) = 4 x g ( x ) = ( x + 2 ) 2

Got questions? Get instant answers now!

h ( x ) = 1 2 x 3 3

sample: f ( x ) = x 3 g ( x ) = 1 2 x 3

Got questions? Get instant answers now!

h ( x ) = 1 ( 3 x 2 4 ) 3

Got questions? Get instant answers now!

h ( x ) = 3 x 2 x + 5 4

sample: f ( x ) = x 4 g ( x ) = 3 x 2 x + 5

Got questions? Get instant answers now!

Questions & Answers

what is the VA Ha D R X int Y int of f(x) =x²+4x+4/x+2 f(x) =x³-1/x-1
Shadow Reply
can I get help with this?
Wayne
Are they two separate problems or are the two functions a system?
Wilson
Also, is the first x squared in "x+4x+4"
Wilson
x^2+4x+4?
Wilson
thank you
Wilson
Please see ***imgur.com/a/lpTpDZk for solutions
Wilson
f(x)=x square-root 2 +2x+1 how to solve this value
Marjun Reply
factor or use quadratic formula
Wilson
what is algebra
Ige Reply
The product of two is 32. Find a function that represents the sum of their squares.
Paul
if theta =30degree so COS2 theta = 1- 10 square theta upon 1 + tan squared theta
Martin Reply
how to compute this 1. g(1-x) 2. f(x-2) 3. g (-x-/5) 4. f (x)- g (x)
Yanah Reply
hi
John
hi
Grace
what sup friend
John
not much For functions, there are two conditions for a function to be the inverse function:   1--- g(f(x)) = x for all x in the domain of f     2---f(g(x)) = x for all x in the domain of g Notice in both cases you will get back to the  element that you started with, namely, x.
Grace
sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
acha se dhek ke bata sin theta ke value
Ajay
sin theta ke ja gha sin square theta hoga
Ajay
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
False statement so you cannot prove it
Wilson
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn
what's the derivative of 4x^6
Axmed Reply
24x^5
James
10x
Axmed
24X^5
Taieb
comment écrire les symboles de math par un clavier normal
SLIMANE
Practice Key Terms 1

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask