<< Chapter < Page Chapter >> Page >

For the following exercises, use function composition to verify that f ( x ) and g ( x ) are inverse functions.

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

  f ( g ( x ) ) = x , g ( f ( x ) ) = x

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Graphical

For the following exercises, use a graphing utility to determine whether each function is one-to-one.

f ( x ) = −5 x + 1

one-to-one

Got questions? Get instant answers now!

For the following exercises, determine whether the graph represents a one-to-one function.

For the following exercises, use the graph of f shown in [link] .

Graph of a line.

Find f 1 ( 0 ) .

2

Got questions? Get instant answers now!

Solve f 1 ( x ) = 0.

Got questions? Get instant answers now!

For the following exercises, use the graph of the one-to-one function shown in [link] .

Graph of a square root function.

Sketch the graph of f 1 .

Graph of a square root function and its inverse.
Got questions? Get instant answers now!

Find f ( 6 )  and  f 1 ( 2 ) .

Got questions? Get instant answers now!

If the complete graph of f is shown, find the domain of f .

[ 2 , 10 ]

Got questions? Get instant answers now!

If the complete graph of f is shown, find the range of f .

Got questions? Get instant answers now!

Numeric

For the following exercises, evaluate or solve, assuming that the function f is one-to-one.

If f ( 6 ) = 7 , find f 1 ( 7 ) .

6

Got questions? Get instant answers now!

If f ( 3 ) = 2 , find f 1 ( 2 ) .

Got questions? Get instant answers now!

If f 1 ( 4 ) = 8 , find f ( 8 ) .

4

Got questions? Get instant answers now!

If f 1 ( 2 ) = 1 , find f ( 1 ) .

Got questions? Get instant answers now!

For the following exercises, use the values listed in [link] to evaluate or solve.

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

Find f 1 ( 0 ) .

1

Got questions? Get instant answers now!

Solve f 1 ( x ) = 7.

Got questions? Get instant answers now!

Use the tabular representation of f in [link] to create a table for f 1 ( x ) .

x 3 6 9 13 14
f ( x ) 1 4 7 12 16
x 1 4 7 12 16
f 1 ( x ) 3 6 9 13 14
Got questions? Get instant answers now!

Technology

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

f ( x ) = x 3 1

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

Graph of a cubic function and its inverse.
Got questions? Get instant answers now!

Find the inverse function of f ( x ) = 1 x 1 . Use a graphing utility to find its domain and range. Write the domain and range in interval notation.

Got questions? Get instant answers now!

Real-world applications

To convert from x degrees Celsius to y degrees Fahrenheit, we use the formula f ( x ) = 9 5 x + 32. Find the inverse function, if it exists, and explain its meaning.

f 1 ( x ) = 5 9 ( x 32 ) . Given the Fahrenheit temperature, x , this formula allows you to calculate the Celsius temperature.

Got questions? Get instant answers now!

The circumference C of a circle is a function of its radius given by C ( r ) = 2 π r . Express the radius of a circle as a function of its circumference. Call this function r ( C ) . Find r ( 36 π ) and interpret its meaning.

Got questions? Get instant answers now!

A car travels at a constant speed of 50 miles per hour. The distance the car travels in miles is a function of time, t , in hours given by d ( t ) = 50 t . Find the inverse function by expressing the time of travel in terms of the distance traveled. Call this function t ( d ) . Find t ( 180 ) and interpret its meaning.

t ( d ) = d 50 , t ( 180 ) = 180 50 . The time for the car to travel 180 miles is 3.6 hours.

Got questions? Get instant answers now!

Chapter review exercises

Functions and Function Notation

For the following exercises, determine whether the relation is a function.

{ ( a , b ) , ( c , d ) , ( e , d ) }

function

Got questions? Get instant answers now!

{ ( 5 , 2 ) , ( 6 , 1 ) , ( 6 , 2 ) , ( 4 , 8 ) }

Got questions? Get instant answers now!

y 2 + 4 = x , for x the independent variable and y the dependent variable

not a function

Got questions? Get instant answers now!

Is the graph in [link] a function?

Graph of a parabola.
Got questions? Get instant answers now!

For the following exercises, evaluate the function at the indicated values: f ( 3 ) ; f ( 2 ) ; f ( a ) ; f ( a ) ; f ( a + h ) .

f ( x ) = 2 x 2 + 3 x

f ( 3 ) = 27 ; f ( 2 ) = 2 ; f ( a ) = 2 a 2 3 a ;
f ( a ) = 2 a 2 3 a ; f ( a + h ) = 2 a 2 + 3 a 4 a h + 3 h 2 h 2

Got questions? Get instant answers now!

f ( x ) = 2 | 3 x 1 |

Got questions? Get instant answers now!

For the following exercises, determine whether the functions are one-to-one.

Questions & Answers

sin^4+sin^2=1, prove that tan^2-tan^4+1=0
SAYANTANI Reply
what is the formula used for this question? "Jamal wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?"
Kuz Reply
i don't need help solving it I just need a memory jogger please.
Kuz
A = P(1 + r/n) ^rt
Dale
how to solve an expression when equal to zero
Mintah Reply
its a very simple
Kavita
gave your expression then i solve
Kavita
Hy guys, I have a problem when it comes on solving equations and expressions, can you help me 😭😭
Thuli
Tomorrow its an revision on factorising and Simplifying...
Thuli
ok sent the quiz
kurash
send
Kavita
Hi
Masum
What is the value of log-1
Masum
the value of log1=0
Kavita
Log(-1)
Masum
What is the value of i^i
Masum
log -1 is 1.36
kurash
No
Masum
no I m right
Kavita
No sister.
Masum
no I m right
Kavita
tan20°×tan30°×tan45°×tan50°×tan60°×tan70°
Joju Reply
jaldi batao
Joju
Find the value of x between 0degree and 360 degree which satisfy the equation 3sinx =tanx
musah Reply
what is sine?
tae Reply
what is the standard form of 1
Sanjana Reply
1×10^0
Akugry
Evalute exponential functions
Sujata Reply
30
Shani
The sides of a triangle are three consecutive natural number numbers and it's largest angle is twice the smallest one. determine the sides of a triangle
Jaya Reply
Will be with you shortly
Inkoom
3, 4, 5 principle from geo? sounds like a 90 and 2 45's to me that my answer
Neese
answer is 2, 3, 4
Gaurav
prove that [a+b, b+c, c+a]= 2[a b c]
Ashutosh Reply
can't prove
Akugry
i can prove [a+b+b+c+c+a]=2[a+b+c]
this is simple
Akugry
hi
Stormzy
x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0
HERVE Reply
x exposent4+4x exposent3+8x exposent2+4x+1=0
HERVE
How can I solve for a domain and a codomains in a given function?
Oliver Reply
ranges
EDWIN
Thank you I mean range sir.
Oliver
proof for set theory
Kwesi Reply
don't you know?
Inkoom
find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad
Martina Reply
factoring polynomial
Noven Reply
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