<< Chapter < Page Chapter >> Page >

h ( x ) = ( 8 + x 3 8 x 3 ) 4

Got questions? Get instant answers now!

h ( x ) = 2 x + 6

sample: f ( x ) = x g ( x ) = 2 x + 6

Got questions? Get instant answers now!

h ( x ) = ( 5 x 1 ) 3

Got questions? Get instant answers now!

h ( x ) = x 1 3

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

Got questions? Get instant answers now!

h ( x ) = 1 ( x 2 ) 3

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

sample: f ( x ) = x g ( x ) = 2 x 1 3 x + 4

Got questions? Get instant answers now!

Graphical

For the following exercises, use the graphs of f , shown in [link] , and g , shown in [link] , to evaluate the expressions.

Graph of a function.
Graph of a function.

For the following exercises, use graphs of f ( x ) , shown in [link] , g ( x ) , shown in [link] , and h ( x ) , shown in [link] , to evaluate the expressions.

Graph of a parabola.
Graph of a square root function.

f ( g ( f ( 2 ) ) )

4

Got questions? Get instant answers now!

Numeric

For the following exercises, use the function values for f  and  g shown in [link] to evaluate each expression.

x f ( x ) g ( x )
0 7 9
1 6 5
2 5 6
3 8 2
4 4 1
5 0 8
6 2 7
7 1 3
8 9 4
9 3 0

For the following exercises, use the function values for f  and  g shown in [link] to evaluate the expressions.

x f ( x ) g ( x )
−3 11 −8
−2 9 −3
−1 7 0
0 5 1
1 3 0
2 1 −3
3 −1 −8

For the following exercises, use each pair of functions to find f ( g ( 0 ) ) and g ( f ( 0 ) ) .

f ( x ) = 4 x + 8 , g ( x ) = 7 x 2

Got questions? Get instant answers now!

f ( x ) = 5 x + 7 , g ( x ) = 4 2 x 2

f ( g ( 0 ) ) = 27 , g ( f ( 0 ) ) = 94

Got questions? Get instant answers now!

f ( x ) = x + 4 , g ( x ) = 12 x 3

Got questions? Get instant answers now!

f ( x ) = 1 x + 2 , g ( x ) = 4 x + 3

f ( g ( 0 ) ) = 1 5 , g ( f ( 0 ) ) = 5

Got questions? Get instant answers now!

For the following exercises, use the functions f ( x ) = 2 x 2 + 1 and g ( x ) = 3 x + 5 to evaluate or find the composite function as indicated.

f ( g ( x ) )

18 x 2 + 60 x + 51

Got questions? Get instant answers now!

( g g ) ( x )

g g ( x ) = 9 x + 20

Got questions? Get instant answers now!

Extensions

For the following exercises, use f ( x ) = x 3 + 1 and g ( x ) = x 1 3 .

Find ( f g ) ( x ) and ( g f ) ( x ) . Compare the two answers.

Got questions? Get instant answers now!

Find ( f g ) ( 2 ) and ( g f ) ( 2 ) .

2

Got questions? Get instant answers now!

What is the domain of ( g f ) ( x ) ?

Got questions? Get instant answers now!

What is the domain of ( f g ) ( x ) ?

( , )

Got questions? Get instant answers now!

Let f ( x ) = 1 x .

  1. Find ( f f ) ( x ) .
  2. Is ( f f ) ( x ) for any function f the same result as the answer to part (a) for any function? Explain.
Got questions? Get instant answers now!

For the following exercises, let F ( x ) = ( x + 1 ) 5 , f ( x ) = x 5 , and g ( x ) = x + 1.

True or False: ( g f ) ( x ) = F ( x ) .

False

Got questions? Get instant answers now!

True or False: ( f g ) ( x ) = F ( x ) .

Got questions? Get instant answers now!

For the following exercises, find the composition when f ( x ) = x 2 + 2 for all x 0 and g ( x ) = x 2 .

( f g ) ( 6 ) ; ( g f ) ( 6 )

( f g ) ( 6 ) = 6 ; ( g f ) ( 6 ) = 6

Got questions? Get instant answers now!

( g f ) ( a ) ; ( f g ) ( a )

Got questions? Get instant answers now!

( f g ) ( 11 ) ; ( g f ) ( 11 )

( f g ) ( 11 ) = 11 , ( g f ) ( 11 ) = 11

Got questions? Get instant answers now!

Real-world applications

The function D ( p ) gives the number of items that will be demanded when the price is p . The production cost C ( x ) is the cost of producing x items. To determine the cost of production when the price is $6, you would do which of the following?

  1. Evaluate D ( C ( 6 ) ) .
  2. Evaluate C ( D ( 6 ) ) .
  3. Solve D ( C ( x ) ) = 6.
  4. Solve C ( D ( p ) ) = 6.
Got questions? Get instant answers now!

The function A ( d ) gives the pain level on a scale of 0 to 10 experienced by a patient with d milligrams of a pain-reducing drug in her system. The milligrams of the drug in the patient’s system after t minutes is modeled by m ( t ) . Which of the following would you do in order to determine when the patient will be at a pain level of 4?

  1. Evaluate A ( m ( 4 ) ) .
  2. Evaluate m ( A ( 4 ) ) .
  3. Solve A ( m ( t ) ) = 4.
  4. Solve m ( A ( d ) ) = 4.

c

Got questions? Get instant answers now!

A store offers customers a 30% discount on the price x of selected items. Then, the store takes off an additional 15% at the cash register. Write a price function P ( x ) that computes the final price of the item in terms of the original price x . (Hint: Use function composition to find your answer.)

Got questions? Get instant answers now!

A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r ( t ) = 25 t + 2 , find the area of the ripple as a function of time. Find the area of the ripple at t = 2.

A ( t ) = π ( 25 t + 2 ) 2 and A ( 2 ) = π ( 25 4 ) 2 = 2500 π square inches

Got questions? Get instant answers now!

A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r ( t ) = 2 t + 1 , express the area burned as a function of time, t (minutes).

Got questions? Get instant answers now!

Use the function you found in the previous exercise to find the total area burned after 5 minutes.

A ( 5 ) = π ( 2 ( 5 ) + 1 ) 2 = 121 π square units

Got questions? Get instant answers now!

The radius r , in inches, of a spherical balloon is related to the volume, V , by r ( V ) = 3 V 4 π 3 . Air is pumped into the balloon, so the volume after t seconds is given by V ( t ) = 10 + 20 t .

  1. Find the composite function r ( V ( t ) ) .
  2. Find the exact time when the radius reaches 10 inches.
Got questions? Get instant answers now!

The number of bacteria in a refrigerated food product is given by N ( T ) = 23 T 2 56 T + 1 , 3 < T < 33 , where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T ( t ) = 5 t + 1.5 , where t is the time in hours.

  1. Find the composite function N ( T ( t ) ) .
  2. Find the time (round to two decimal places) when the bacteria count reaches 6752.

a. N ( T ( t ) ) = 23 ( 5 t + 1.5 ) 2 56 ( 5 t + 1.5 ) + 1 ; b. 3.38 hours

Got questions? Get instant answers now!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 1

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask