<< Chapter < Page Chapter >> Page >

f ( x ) = 9 + 2 x 3

f −1 ( x ) = ( x 9 2 ) 3

Got questions? Get instant answers now!

f ( x ) = 2 x + 8

f −1 ( x ) = 2 8 x x

Got questions? Get instant answers now!

f ( x ) = x + 3 x + 7

f −1 ( x ) = 7 x 3 1 x

Got questions? Get instant answers now!

f ( x ) = 3 x + 4 5 4 x

f −1 ( x ) = 5 x 4 4 x + 3

Got questions? Get instant answers now!

f ( x ) = 5 x + 1 2 5 x

Got questions? Get instant answers now!

f ( x ) = x 2 + 2 x ,   [ −1 , )

f −1 ( x ) = x + 1 1

Got questions? Get instant answers now!

f ( x ) = x 2 + 4 x + 1 ,   [ −2 , )

Got questions? Get instant answers now!

f ( x ) = x 2 6 x + 3 ,   [ 3 , )

f −1 ( x ) = x + 6 + 3

Got questions? Get instant answers now!

Graphical

For the following exercises, find the inverse of the function and graph both the function and its inverse.

f ( x ) = x 2 + 2 , x 0

Got questions? Get instant answers now!

f ( x ) = 4 x 2 , x 0

f 1 ( x ) = 4 x

Graph of f(x)=4- x^2 and its inverse, f^(-1)(x)= sqrt(4-x).
Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

f ( x ) = ( x 4 ) 2 , x 4

f 1 ( x ) = x + 4

Graph of f(x)= (x-4)^2 and its inverse, f^(-1)(x)= sqrt(x)+4.
Got questions? Get instant answers now!

f ( x ) = 1 x 3

f 1 ( x ) = 1 x 3

Graph of f(x)= 1-x^3 and its inverse, f^(-1)(x)= (1-x)^(1/3).
Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

f ( x ) = x 2 6 x + 1 , x 3

f 1 ( x ) = x + 8 + 3

Graph of f(x)= x^2-6x+1 and its inverse, f^(-1)(x)= sqrt(x+8)+3.
Got questions? Get instant answers now!

f ( x ) = 1 x 2 , x 0

f 1 ( x ) = 1 x

Graph of f(x)= 1/x^2 and its inverse, f^(-1)(x)= sqrt(1/x).
Got questions? Get instant answers now!

For the following exercises, use a graph to help determine the domain of the functions.

f ( x ) = ( x + 1 ) ( x 1 ) x

Got questions? Get instant answers now!

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

[ 2 , 1 ) [ 3 , )

Graph of f(x)= sqrt((x+2)(x-3)/(x-1)).
Got questions? Get instant answers now!

f ( x ) = x ( x + 3 ) x 4

Got questions? Get instant answers now!

f ( x ) = x 2 x 20 x 2

[ 4 , 2 ) [ 5 , )

Graph of f(x)= sqrt((x^2-x-20)/(x-2)).
Got questions? Get instant answers now!

f ( x ) = 9 x 2 x + 4

Got questions? Get instant answers now!

Technology

For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on the graph of the inverse with y -coordinates given.

f ( x ) = x 3 x 2 , y = 1 , 2 , 3

( 2 ,   0 ) ;   ( 4 ,   2 ) ;   ( 22 ,   3 )

Graph of f(x)= x^3-x-2.
Got questions? Get instant answers now!

f ( x ) = x 3 + x 2 , y = 0 , 1 , 2

Got questions? Get instant answers now!

f ( x ) = x 3 + 3 x 4 , y = 0 , 1 , 2

( 4 ,   0 ) ;   ( 0 ,   1 ) ;   ( 10 ,   2 )

Graph of f(x)= x^3+3x-4.
Got questions? Get instant answers now!

f ( x ) = x 3 + 8 x 4 , y = 1 , 0 , 1

Got questions? Get instant answers now!

f ( x ) = x 4 + 5 x + 1 , y = 1 , 0 , 1

( 3 ,   1 ) ;   ( 1 ,   0 ) ;   ( 7 ,   1 )

Graph of f(x)= x^4+5x+1.
Got questions? Get instant answers now!

Extensions

For the following exercises, find the inverse of the functions with a , b , c positive real numbers.

f ( x ) = x 2 + b x

f 1 ( x ) = x + b 2 4 b 2

Got questions? Get instant answers now!

f ( x ) = a x + b 3

f 1 ( x ) = x 3 b a

Got questions? Get instant answers now!

Real-world applications

For the following exercises, determine the function described and then use it to answer the question.

An object dropped from a height of 200 meters has a height, h ( t ) , in meters after t seconds have lapsed, such that h ( t ) = 200 4.9 t 2 . Express t as a function of height, h , and find the time to reach a height of 50 meters.

t ( h ) = 200 h 4.9 , 5.53 seconds

Got questions? Get instant answers now!

An object dropped from a height of 600 feet has a height, h ( t ) , in feet after t seconds have elapsed, such that h ( t ) = 600 16 t 2 . Express t as a function of height h , and find the time to reach a height of 400 feet.

Got questions? Get instant answers now!

The volume, V , of a sphere in terms of its radius, r , is given by V ( r ) = 4 3 π r 3 . Express r as a function of V , and find the radius of a sphere with volume of 200 cubic feet.

r ( V ) = 3 V 4 π 3 , 3.63 feet

Got questions? Get instant answers now!

The surface area, A , of a sphere in terms of its radius, r , is given by A ( r ) = 4 π r 2 . Express r as a function of V , and find the radius of a sphere with a surface area of 1000 square inches.

Got questions? Get instant answers now!

A container holds 100 mL of a solution that is 25 mL acid. If n mL of a solution that is 60% acid is added, the function C ( n ) = 25 + .6 n 100 + n gives the concentration, C , as a function of the number of mL added, n . Express n as a function of C and determine the number of mL that need to be added to have a solution that is 50% acid.

n ( C ) = 100 C 25 .6 C , 250 mL

Got questions? Get instant answers now!

The period T , in seconds, of a simple pendulum as a function of its length l , in feet, is given by T ( l ) = 2 π l 32.2 . Express l as a function of T and determine the length of a pendulum with period of 2 seconds.

Got questions? Get instant answers now!

The volume of a cylinder , V , in terms of radius, r , and height, h , is given by V = π r 2 h . If a cylinder has a height of 6 meters, express the radius as a function of V and find the radius of a cylinder with volume of 300 cubic meters.

r ( V ) = V 6 π , 3.99 meters

Got questions? Get instant answers now!

The surface area, A , of a cylinder in terms of its radius, r , and height, h , is given by A = 2 π r 2 + 2 π r h . If the height of the cylinder is 4 feet, express the radius as a function of V and find the radius if the surface area is 200 square feet.

Got questions? Get instant answers now!

The volume of a right circular cone, V , in terms of its radius, r , and its height, h , is given by V = 1 3 π r 2 h . Express r in terms of h if the height of the cone is 12 feet and find the radius of a cone with volume of 50 cubic inches.

r ( V ) = V 4 π , 1.99 inches

Got questions? Get instant answers now!

Consider a cone with height of 30 feet. Express the radius, r , in terms of the volume, V , and find the radius of a cone with volume of 1000 cubic feet.

Got questions? Get instant answers now!
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