Deck 6: Exponential and Logarithmic Functions

Question 1

For the given functions f and g, find the requested composite function value.
, g(x)= 16x - 3; Find (f ∘ g)(7).

A)106,602
B)6,717
C)99,885
D)45,780

Answer 1

106,602

Question 2

For the given functions f and g, find the requested composite function value.
g(x)= Find (g ∘ f)(-2).

A)25
B)13
C)
D)

Answer 2

25

Question 3

For the given functions f and g, find the requested composite function value.
; Find (g ∘ g)(1).

A)199
B)16
C)67
D)10

Answer 3

199

Question 4

For the given functions f and g, find the requested composite function.
f(x)= , g(x)= 3x + 5; Find (g ∘ f)(x).

A)x
B)3x + 10
C)x + 10
D)

Question 5

For the given functions f and g, find the requested composite function value.
f(t)= , Find (f ∘ g)(9).

A)25
B)31
C)625
D)360

Question 6

For the given functions f and g, find the requested composite function value.
f(x)= 2x + 6, g(x)= ; Find

A)16,901
B)136
C)785
D)34

Question 7

Evaluate the expression using the values given in the table.

A)-7
B)4
C)-2
D)11

Question 8

For the given functions f and g, find the requested composite function.
f(x)= g(x)= 8x - 12; Find (f ∘ g)(x).

A)
B)
C)
D)

Question 9

For the given functions f and g, find the requested composite function.
f(x)= , g(x)= 4x - 3; Find (g ∘ f)(x).

A)
B)
C)
D)

Question 10

For the given functions f and g, find the requested composite function.
f(x)= 3x + 8, g(x)= 3x - 1; Find (f ∘ g)(x).

A)9x + 5
B)9x + 11
C)9x + 7
D)9x + 23

Question 11

For the given functions f and g, find the requested composite function.
f(x)= , g(x)= ; Find (f ∘ g)(x).

A)
B)
C)
D)

Question 12

For the given functions f and g, find the requested composite function.
g(x)= 5x + 2; Find (g ∘ f)(x).

A)x
B)5x + 8
C)x + 4
D)

Question 13

For the given functions f and g, find the requested composite function value.
f(x)= 7x + 8, g(x)= Find (g ∘ f)(3).

A)-
B)
C)
D)

Question 14

For the given functions f and g, find the requested composite function.
f(x)= -2x + 5, g(x)= 5x + 3; Find (g ∘ f)(x).

A)-10x + 28
B)-10x + 11
C)10x + 28
D)-10x - 22

Question 15

Evaluate the expression using the values given in the table.

A)1
B)8
C)7
D)Undefined

Question 16

For the given functions f and g, find the requested composite function value.
f(x)= 4x + 6, ; Find (f ∘ g)(0).

A)26
B)149
C)30
D)105

Question 17

Evaluate the expression using the graphs of y = f(x)and y = g(x).
Evaluate (fg)(1).

A)6
B)-5
C)3
D)0

Question 18

For the given functions f and g, find the requested composite function value.
, g(x)= 15x - 8; Find (f ∘ g)(7).

A)121,929
B)9,127
C)112,802
D)59,073

Question 19

For the given functions f and g, find the requested composite function value.
g(x)= 3x; Find (f ∘ g)(3).

A)
B)
C)
D)

Question 20

For the given functions f and g, find the requested composite function.
, g(x)= ; Find (f ∘ g)(x).

A)
B)
C)
D)

Question 21

Find functions f and g so that f ∘ g = H.
H(x)=

A)
B)
C)
D)

Question 22

Solve the problem.
The population P of a predator mammal depends upon the number x of a smaller animal that is itsprimary food source. The population s of the smaller animal depends upon the amount a of a certain plantthat is its primary food source. If and , what is the relationship between thepredator mammal and the plant food source?

A)
B)
C)
D)

Question 23

Find functions f and g so that f ∘ g = H.
H(x)=

A)
B)
C)f
D)

Question 24

Solve the problem.
An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle.At any time t, in minutes, after the beginning of the leak, the radius of the oil slick on the surface isr(t)= 4t ft. Find the area A of the oil slick as a function of time.

A)
B)
C)
D)

Question 25

Find functions f and g so that f ∘ g = H.
H(x)=

A)
B)
C)
D)

Question 26

Find functions f and g so that f ∘ g = H.
H(x)=

A)
B)
C)
D)

Question 27

For the given functions f and g, find the requested composite function.
f(x)= x , g(x)= ; Find (f ∘ g)(x).

A)
B)
C)
D)

Question 28

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.
f(x)= , g(x)=

A)No, no
B)No, yes
C)Yes, no
D)Yes, yes

Question 29

Find functions f and g so that f ∘ g = H.
H(x)=

A)f(x)= , g(x)=
B)f(x)= ; g(x)=
C)f(x)= ; g(x)=
D)f(x)= ; g(x)= - 9

Question 30

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.
f(x)= , g(x)=

A)Yes, yes
B)No, no
C)No, yes
D)Yes, no

Question 31

Find functions f and g so that f ∘ g = H.
H(x)=

A)
B)
C)
D)

Question 32

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.
f(x)= , g(x)=

A)Yes, yes
B)No, no
C)No, yes
D)Yes, no

Question 33

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.
f(x)= , g(x)= x

A)No, no
B)No, yes
C)Yes, no
D)Yes, yes

Question 34

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.
f(x)= , g(x)=

A)Yes, yes
B)No, no
C)No, yes
D)Yes, no

Question 35

Find functions f and g so that f ∘ g = H.
H(x)= ∣

A)f(x)= ∣ ; g(x)= 8x + 8
B)f(x)= g(x)= 8x + 8
C)f(x)= g(x)= 8x - 8
D)f(x)= x; g(x)= 8x + 8

Question 36

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.
f(x)= , g(x)= 4x - 7

A)Yes, yes
B)No, no
C)Yes, no
D)No, yes

Question 37

Find functions f and g so that f ∘ g = H.
H(x)=

A)
B)
C)
D)

Question 38

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.
f(x)= 4x, g(x)=

A)Yes, yes
B)No, no
C)Yes, no
D)No, yes

Question 39

Find functions f and g so that f ∘ g = H.
H(x)=

A)f(x)= ; g(x)= x + 1
B)f(x)= x + 1 ; g(x)=
C)f(x)= ; g(x)= 1
D)f(x)= g(x)= x + 1

Question 40

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.
f(x)= , g(x)=

A)No, no
B)No, yes
C)Yes, no
D)Yes, yes

Question 41

Find the domain of the composite function f ∘ g.
f(x)= ; g(x)=

A)
B)
C)
D)

Question 42

Write the word or phrase that best completes each statement or answers the question.
If and g(x)= 2x - a, find a so that the graph of f ∘ g crosses the y-axis at 36.

Question 43

Find the domain of the composite function f ∘ g.
f(x)= x + 4; g(x)=

A)
B)
C)
D)

Question 44

Indicate whether the function is one-to-one.
{(-10, 4), (-15, 4), (-16, 1)}

A)Yes
B)No

Question 45

Find the domain of the composite function f ∘ g.
f(x)= ; g(x)=

A)
B)
C)
D)

Question 46

Find the domain of the composite function f ∘ g.
f(x)= ; g(x)=

A)
B)
C)
D)

Question 47

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
If f(x)= and g(x)= -1 + 5x, find (f ∘g)(x)and find the domain of (f ∘ g)(x).

Question 48

Find the domain of the composite function f ∘ g.

A)
B)all real numbers
C)
D)

Question 49

Find the domain of the composite function f ∘ g.

A)
B)
C)
D)

Question 50

Find the domain of the composite function f ∘ g.
f(x)= g(x)= 2x + 4

A)
B)
C)
D)

Question 51

Write the word or phrase that best completes each statement or answers the question.
The volume V (in cubic inches)of a cylindrical pipe with length 12 inches is given by V where ris the radius of the piston (in inches). If the radius is increasing with time t (in minutes)according to theformula find the volume V of the pipe as a function of the time t.

Question 52

Solve the problem.
The surface area of a balloon is given by where r is the radius of the balloon. If the radius isincreasing with time t, as the balloon is being blown up, according to the formula find thesurface area S as a function of the time t.

A)
B)
C)
D)

Question 53

Write the word or phrase that best completes each statement or answers the question.
The surface area S (in square inches)of a cylindrical pipe with length 12 inches is given by πr, where r is the radius of the piston (in inches). If the radius is increasing with time t (in minutes)according to the formula , find the surface area S of the pipe as a function of the time t.

Question 54

Find the domain of the composite function f ∘ g.
f(x)= 7x + 42; g(x)= x + 10

A)
B)
C)
D)

Question 55

Indicate whether the function is one-to-one.
{(14, -17), (13, -6), (-16, -2)}

A)Yes
B)No

Question 56

Write the word or phrase that best completes each statement or answers the question.
The price p of a certain product and the quantity sold x obey the demand equation 300. Suppose that the cost C of producing x units is Assuming that all items produced aresold, find the cost C as a function of the price p.

Question 57

Find the domain of the composite function f ∘ g.
f(x)= ; g(x)=

A)
B)
C)
D)

Question 58

Solve the problem.
An airline charter service charges a fare per person of $200 plus $20 for each unsold seat. The airplaneholds 200 passengers. Let x represent the number of unsold seats and write an expression for the totalrevenue R for a charter flight.

A)R(x)= (200 - x)(200 + 20x)or 40,000 + 3,800x -
B)R(x)= 200(200 + 20x)or 40,000 + 4,000x
C)R(x)= (200 - x)(200 + 20x)or 40,000 + 4,000x -
D)R(x)= x(200 + 20x)or 200x +

Question 59

Find the domain of the composite function f ∘ g.
f(x)= 3x + 3; g(x)=

A)
B)
C)
D)

Question 60

Find the domain of the composite function f ∘ g.
f(x)= ; g(x)=

A)
B)
C)
D)

Question 61

Use the horizontal line test to determine whether the function is one -to-one.

A)Yes
B)No

Question 62

Use the horizontal line test to determine whether the function is one -to-one.

A)Yes
B)No

Question 63

Find the inverse of the function and state its domain and range .
{(6, -2), (2, -6), (8, -8), (-8, 8)}

A){(-2, 6), (-6, 2), (-8, 8), (8, -8)} D = {-2, -6, -8, 8}; R = {6, 2, 8, -8}
B) D = { 6, 2, 8, -8}, R =
C){(8, 8), (8, 2), (-2, 6), (-8, -8)}; D = {8, 8, -2, -8}; R = {8, 2, 6, -8}
D){(8, 8), (-6, 2), (-2, 2), (-8, -8)}; D = {(8, -6, -2, -8}; R = {8, 2, -8}

Question 64

Decide whether or not the functions are inverses of each other.
f(x)= 4x + 16, g(x)=

A)Yes
B)No

Question 65

The graph of a one-to-one function f is given. Draw the graph of the inverse function f as a dashed line or curve.

A)
B)

Question 66

Decide whether or not the functions are inverses of each other.
f(x)= 9x - 6, g(x)=

A)No
B)Yes

Question 67

Indicate whether the function is one-to-one.
{(5, -3), (3, -5), (-4, 9), (4, -9)}

A)Yes
B)No

Question 68

The graph of a one-to-one function f is given. Draw the graph of the inverse function f as a dashed line or curve.
f(x)= 4x

A)
B)

Question 69

Indicate whether the function is one-to-one.
{(-5, -9), (-4, -9), (-3, 7), (-2, 4)}

A)Yes
B)No

Question 70

Find the inverse. Determine whether the inverse represents a function.
{(6, -10), (-4, -9), (-6, -8), (-8, -7)}

A){(-10, 6), (-9, -4), (-8, -6), (-7, -8)}; a function
B){(-10, 6), (-9, -4), (-8, -6), (-7, -8)}; not a function
C){(-9, -10), (-10, -6), (6, -4), (-9, -8)}; not a function
D){(-9, -10), (-7, -6), (6, -6), (-9, -8)}; a function

Question 71

Use the horizontal line test to determine whether the function is one -to-one.

A)Yes
B)No

Question 72

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the
graph of y = x is also given.

A)
B)
C)
D)

Question 73

The graph of a one-to-one function f is given. Draw the graph of the inverse function f as a dashed line or curve.

A)
B)

Question 74

Use the horizontal line test to determine whether the function is one -to-one.

A)Yes
B)No

Question 75

The graph of a one-to-one function f is given. Draw the graph of the inverse function f as a dashed line or curve.

A) Function is its own inverse
B)

Question 76

Indicate whether the function is one-to-one.
{(6, -4), (9, -3), (7, -2), (5, -1)}

A)Yes
B)No

Question 77

Find the inverse of the function and state its domain and range .
{(-3, 4), (-1, 5), (0, 2), (2, 6), (5, 7)}

A){(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)} D = {2, 4, 5, 6, 7}; R = {-3, -1, 0, 2, 5}
B){(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {2, 4, 5, 6, 7}
C){(-3, -4), (-1, -5), (0, -2), (2, -6), (5, -7)}; D = {-3, -1, 0, 2, 5}; R = {-7, -6, -5, -4, -2}
D){(3, -4), (1, -5), (0, -2), (-2, -6), (-5, -7)}; D = {3, 1, 0, -2, -5}; R = {-7, -6, -5, -4, -2}

Question 78

Find the inverse of the function and state its domain and range .
{(7, 2), (5, 3), (3, 4), (1, 5)}

A){(2, 7), (3, 5), (4, 3), (5, 1)}; D = {2, 3, 4, 5 }; R = {7, 5, 3, 1}
B)
C){(3, 2), (2, 3), (7, 5), (3, 4)}; D = {(3, 2, 7}; R = {(2, 3 5, 4}
D){(3, 2), (5, 3), (7, 3), (3, 4)}; D = {3, 5, 7}; R = {2, 3, 4}

Question 79

Use the horizontal line test to determine whether the function is one -to-one.

A)Yes
B)No

Question 80

Use the horizontal line test to determine whether the function is one -to-one.

A)Yes
B)No