Find the inverse of the one–to–one function.
51)
51)
f(x) = – 5x + 4
A)
f–1(x) =y – 4
–5
B)
f–1(x) =x + 4
–5
C)
f–1(x) =
–5x – 4
–5
D)
f–1(x) =x – 4
–5
Find the requested value.
52)
f(x) =4x – 3, g(x) =4x2+ 14x + 4
Find f
g(–4).
52)
A)
4
12
B)
– 4
13
C)
4
D)
–19
12
Find the indicated function value.
53)
f(x) =3x2+ 3x + 6, g(x) =4x – 1
Find (f + g)(–5).
53)
A)
165
B)
–105
C)
45
D)
171
For the pair of functions, determine the domain of f +
g.
54)
f(x) =3x – 9, g(x) =5
x +7
54)
A)
( ,
)
B)
(0,
)
C)
( , –5) or (–5,
)
D)
( , –7) or (–7,
)
Use the graph of f to solve.
55)
55)
Find the range of f.
A)
( ,
)
B)
[0, 4]
C)
[2, 4]
D)
(0, 4)
Find the requested value.
56)
f(x) = – 2x + 3, g(x) = – 5x2– 5x + 3
Find f
g(–2).
56)
A)
1
B)
–1
7
C)
–7
13
D)
– 1
For the pair of functions, determine the domain of f +
g.
57)
57)
f(x) =4x + – 10, g(x) =4x +3
A)
( ,
)(–
,
)
B)
( , 0) or (0,
)
C)
( , –4) or (–4,
)
D)
(0,
)
20
Find the inverse of the one–to–one function.
58)
f(x) =3x +8
x +10
58)
A)
f–1(x) =3x –8
x –10
B)
f–1(x) =x2+10x –8
3
C)
f–1(x) =x +10
3x +8
D)
f–1(x) =10x –8
3– x
59)
59)
f(x) = – 6x
A)
f–1(x) =1
6x
B)
f–1(x) = – 1
6x
C)
f–1(x) =6x
D)
f–1(x) =
–6
x
Solve the problem.
60)
60)
A firm making toaster ovens finds that the total cost, C(x), of producing x units is given by
C(x) =35x +510.
The revenue, R(x), from selling x units is determined by the price per unit times the number of
units sold, thus
R(x) =45x.
Find and interpret (R – C)(71).
A)
$6190 profit, income exceeds cost
B)
$122 profit, income exceeds cost
C)
$200 profit, income exceeds cost
D)
–$200 loss, cost exceeds income
Find the requested value.
61)
61)
f(x) = x + 1, g(x) = x – 5
Find (f + g)(4).
A)
14
B)
2
C)
12
D)
4
Find the indicated function value.
62)
62)
Find f(–9) when f(x) = – 5x – 8.
A)
37
B)
–53
C)
44.2
D)
53
Use the graph to find the value.
63)
f
g(–5)
63)
A)
– 7
B)
–1
7
C)
7
D)
1
7
Find the composition.
64)
If f(x) =x2+ 8 and g(x) =x2– 6, find (g
f)(2).
64)
A)
12
B)
138
C)
48
D)
62
65)
If f(x) =x + 8 and g(x) = 8x – 12, find (f
g)(x).
65)
A)
2 2x + 1
B)
8x – 4
C)
8x + 8 – 12
D)
2 2x – 1
Provide an appropriate response.
66)
If f(x) = – 7x + 5, find f–1(x).
66)
A)
f–1(x) =x + 5
–7
B)
f–1(x) =
–7x – 5
–7
C)
f–1(x) =y – 5
–7
D)
f–1(x) =x – 5
–7
23
Solve the problem.
67)
67)
A research team collected data concerning a local welfare–to–work program. They found that the
more frequently a participant attended weekly group support meetings, the longer he or she
would keep the same job. The data are summarized in the graph below. Call the function f.
Find f–1(40).
A)
80
B)
75
C)
18
D)
67
Use the graph of f to solve.
68)
68)
List the two values of x for which f(x) = 0
A)
3 and 4
B)
3 and –4
C)
–3 and –4
D)
–3 and 4
Decide whether the relation is a function.
69)
69)
{(–3, 6), (–2, 2), (4, 4), (5, –8)}
A)
function
B)
not a function
Find the requested value.
70)
f(x) = – 4x2– 6, g(x) = x – 5
Find (f – g)(3).
70)
A)
–50
B)
–40
C)
39
D)
–34
Use the graph to find the indicated function value.
71)
71)
y = f(x). Find f(–3)
A)
3.5
B)
7
C)
–0.5
D)
2.5
For the pair of functions, determine the domain of f +
g.
72)
f(x) =2x2+ 4, g(x) =5x3– 2
72)
A)
( , 0)
B)
( , 0) or (0,
)
C)
( ,
)
D)
(0,
)
Find the inverse of the one–to–one function.
73)
f(x) =12
x
73)
A)
f–1(x) =12
x
B)
f–1(x) = – 12x
C)
f–1(x) =12x
D)
f–1(x) =x
12
Decide whether the relation is a function.
74)
74)
{(–6, 4), (–1, 5), (1, 1), (1, 7)}
A)
not a function
B)
function
Use the graph of the function to draw the graph of the inverse function.
75)
75)
A)
B)
Decide whether the relation is a function.
76)
76)
{(–5, –2), (–3, –9), (4, –3), (4, –4)}
A)
function
B)
not a function
Find the domain of the function.
77)
f(x) =x2
x2+15
77)
A)
( ,
)
B)
(–15,
)
C)
( , 0) or (0,
)
D)
( , –15) or (–15,
)
Use the graph to find the indicated function value.
78)
78)
y = f(x). Find f(–4)
A)
13
B)
1.75
C)
–4
D)
4
Find the indicated function value.
79)
f(x) =3x + 5, g(x) =3x2+ 4x –3
Find (f + g)(4).
79)
A)
68
B)
66
C)
46
D)
78
28
For the pair of functions, determine the domain of f +
g.
80)
f(x) =5x
x –7, g(x) =3
x +1
80)
A)
( ,
)
B)
( , –7) or (–7, 1) or (1,
)
C)
( , –1) or (7,
)
D)
( , –1) or (–1, 7) or (7,
)
Use the vertical line test to determine whether or not the graph is a graph of a function.
81)
81)
A)
not a function
B)
function
Find the domain of the function.
82)
f(x) =4x
x + 7
82)
A)
( ,
)
B)
( , –7)
C)
( , 0) or (0,
)
D)
( , –7) or (–7,
)
83)
f(x) =
–2x
x + 3
83)
A)
( , –3) or (–3,
)
B)
( ,–3)
C)
( , 0) or (0,
)
D)
( ,
)
Solve the problem.
84)
84)
A firm is considering a new product. The accounting department estimates that the total cost,
C(x), of producing x units will be
C(x) =50x +3590.
The sales department estimates that the revenue, R(x), from selling x units will be
R(x) =60x,
but that no more than 760 units can be sold at that price. Find and interpret (R – C)(760).
A)
$1119 profit, income exceeds cost
It is worth it to develop product.
B)
$87,190 profit, income exceeds cost
It is worth it to develop product.
C)
–$4010 loss, cost exceeds income
It is not worth it to develop product.
D)
$4010 profit, income exceeds cost
It is worth it to develop product.
Find the indicated function value.
85)
f(x) =4x2+ 3, g(x) =3x2–4
Find (f + g)(2).
85)
A)
27
B)
35
C)
11
D)
21
Decide whether the relation is a function.
86)
86)
{(–7, –8), (–5, 8), (1, 5), (3, –4)}
A)
function
B)
not a function
30
Express the interval in set builder notation and graph the interval on a number line.
87)
87)
[–6, 8)
A)
{x –6 x 8 }
B)
{x –6< x 8 }
C)
{x –6 x <8 }
D)
{x x <8 }
Use the graph of the function to draw the graph of the inverse function.
88)
88)
A)
B)
31
Find the indicated function value.
89)
Find f(3) when f(x) =x3+ 6
x2+ 1 .
89)
A)
3
2
B)
11
3
C)
27
10
D)
33
10
Solve the problem.
90)
90)
The regular price of a car is x dollars. Let f(x) = x –600 and g(x) =0.85x. Then f represents the
price of the car less $600, and g represents a 15% discount on the car. Which composite function
represents the greater discount on the car, f
g or g
f?
A)
f
g represents the greater discount.
B)
f
g and g
f represent an equal discount.
C)
g
f represents the greater discount.
D)
f
g and g
f don’t represent discounts on the car.
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
91)
f(x) =x + 5
3 and g(x) =3x + 5
91)
A)
not inverses
B)
inverses
Find the indicated function value.
92)
92)
Find f(5) when f(x) =5.
A)
5
B)
–5
C)
–25
D)
0
Use the vertical line test to determine whether or not the graph is a graph of a function.
93)
93)
A)
function
B)
not a function
Find the composition.
94)
94)
If f(x) =5x +3 and g(x) = x +2, find (g
f)(x).
A)
5x +5
B)
5x2+13
C)
5x +13
D)
5x2+13x +6
Provide an appropriate response.
95)
If f(x) =x2+ 3x and g(x) = x +1, find (f
g)(x) and (g
f)(x).
95)
A)
x2+5x +1; x2+ 3x +1
B)
x2+5x +10; x2+ 3x +1
C)
x2+10; x2+ 3x +1
D)
x2+5x +10; 3x +1
33
Determine whether the relation is a function. Give domain and range of the relation.
96)
96)
{(–2, 7), (1, 4), (4, –5), (6, –1)}
A)
not a function; domain: {7, 4, –5, –1}, range: {–2, 1, 4, 6}
B)
not a function; domain: {–2, 1, 4, 6}, range: {7, 4, –5, –1}
C)
function; domain: {7, 4, –5, –1}, range: {–2, 1, 4, 6}
D)
function; domain: {–2, 1, 4, 6}, range: {7, 4, –5, –1}
Find the indicated function value.
97)
Find f(–2) when f(x) =5x2+ 4x + 1.
97)
A)
11
B)
13
C)
29
D)
–3
Express the interval in set builder notation and graph the interval on a number line.
98)
98)
[–9, 4]
A)
{x –9< x <4 }
B)
{x –9< x 4 }
C)
{x –9 x <4 }
D)
{x –9 x 4 }
Find the indicated function value.
99)
Find f(3) when f(x) =x2+ 4
x3– 6x.
99)
A)
13
9
B)
13
21
C)
13
27
D)
1
The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the
graph to answer the question.
100)
100)
Between what two years is the difference in function values equal to 5%?
A)
between 1990 and 1995
B)
between 1970 and 1975
C)
between 1980 and 1985
D)
between 1995 and 2000
Find the indicated function value.
101)
101)
Find g(a – 1) when g(x) =3x – 4.
A)
3a – 11
B)
3a – 7
C)
3a – 3
D)
3a