44)
{(-8, -5), (5, 8), (9, 9), (–9, -9)}
A)
B)
C)
D)
Find an equation of the inverse of the relation.
45)
y =6x + 5
A)
x =5y + 6
B)
y =5x + 6
C)
D)
x =6y + 5
46)
y =2+ 6x
A)
y =6– 2x
B)
x =6+ 2y
C)
D)
x =2+ 6y
47)
y =7x2+ 4x
A)
x =7y2+ 4y
B)
y =-7x2– 4x
C)
D)
y =4x2+ 7x
21
48)
y =2x3+ 4
A)
y =4x3+ 2
B)
x =2y3 + 4
C)
D)
y =-2x3– 4
Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
49)
y =8x – 6
A)
B)
C)
D)
50)
y =6+ 5x
A)
B)
C)
D)
23
51)
y =2x2+ 4x
A)
B)
C)
D)
24
52)
y =4x3+ 7
A)
B)
C)
D)
Determine whether the function is one–to–one.
53)
f(x) =2x – 4
A)
No
B)
Yes
54)
f(x) = x2+ 3
A)
No
B)
Yes
25
55)
f(x) =7x2+ 3
A)
Yes
B)
No
56)
f(x) = x3– 7
A)
Yes
B)
No
57)
f(x) =3x3– 8
A)
No
B)
Yes
58)
f(x) = 4x2+ x
A)
No
B)
Yes
59)
f(x) =16 –x2
A)
Yes
B)
No
60)
f(x) = |25 – x2|
A)
Yes
B)
No
61)
f(x) =1
7
x
A)
Yes
B)
No
Determine whether the given function is one–to–one. If so, find a formula for the inverse.
62)
f(x) =4x – 3
A)
f–1(x) =x + 3
4
B)
f–1(x) =x
4+ 3
C)
Not a one–to–one function
D)
f–1(x) =x – 3
4
63)
f(x) = x3+ 1
A)
f–1(x) =
3x + 1
B)
Not a one–to–one function
C)
f–1(x) =
3x – 1
D)
f–1(x) =
3x– 1
26
64)
f(x) =5x3+ 3
A)
f–1(x) =3x + 3
5
B)
f–1(x) =3x – 3
5
C)
f–1(x) =3 x
5
– 3
D)
Not a one–to–one function
65)
f(x) =5
x – 4
A)
Not a one–to–one function
B)
f–1(x) =x
-4 + 5x
C)
f–1(x) =4x + 5
x
D)
f–1(x) =-4 + 5x
x
66)
f(x) =3x + 2
A)
Not a one–to–one function
B)
f–1(x) =(x + 2)3
C)
f–1(x) =3x – 2
D)
f–1(x) =x3– 2
67)
f(x) =3x + 8
-6x – 2
A)
f–1(x) =3x + 8
-6x – 2
B)
f–1(x) =2x + 8
-6x – 3
C)
Not a one–to–one function
D)
f–1(x) =-6x – 3
2x + 8
68)
f(x) = (x – 9)2
A)
f–1(x) =1
x + 9
B)
f–1(x) =x+ 9
C)
f–1(x) =x + 9
D)
Not a one–to–one function
Graph the function as a solid curve and its inverse as a dashed curve.
27
69)
f(x) =5x
A)
B)
C)
D)
70)
f(x) =
5
4x + 6
A)
B)
C)
D)
71)
f(x) = x3+ 5
A)
B)
C)
D)
Use composition to verify whether or not the inverse is correct.
72)
f(x) = –
1
8x, f–1(x) = – 8x
A)
No
B)
Yes
73)
f(x) =6x – 4, f–1(x) =x + 6
4
A)
Yes
B)
No
30
74)
f(x) =9x – 9, f–1(x) =1
9x + 1
A)
Yes
B)
No
75)
f(x) =3
x + 7 , f–1(x) =7x + 3
x
A)
No
B)
Yes
76)
f(x) =3x + 9, f–1(x) =1
3x – 3
A)
Yes
B)
No
77)
f(x) =3x + 6, f–1(x) =1
3x – 3
A)
No
B)
Yes
78)
f(x) =x3+8, f–1(x) =3x +8
A)
Yes
B)
No
Solve the problem.
79)
A size 6 dress in Country C is size 36 in Country D. A function that converts dress sizes in Country C to those in
Country D is f(x) = x +30.Find a formula for the inverse of the function described.
A)
f–1(x) = x +30
B)
f–1(x) = x – 30
C)
D)
f–1(x) =x
30
80)
A size –2 dress in Country C is size -20 in Country D. A function that converts dress sizes in Country C to those
in Country D is f(x) = x – 22. Find a formula for the inverse of the function described.
A)
f–1(x) = x + 22
B)
f–1(x) =x
22
C)
D)
f–1(x) = x
-22
81)
A size 10 dress in Country C is size 44 in Country D. A function that converts dress sizes in Country C to those
in Country D is f(x) = 2(x +12). Find a formula for the inverse of the function described.
A)
f–1(x) =x – 12
2
B)
f–1(x) = x – 12
C)
D)
f–1(x) =x
2– 12
82)
A size 38 dress in Country C is size 11 in Country D. A function that converts dress sizes in Country C to those
in Country D is f(x) =x
2– 8. Find a formula for the inverse of the function described.
A)
f–1(x) = 2(x – 8)
B)
f–1(x) = 2x +8
C)
D)
f–1(x) = 2(x +8)
83)
32° Fahrenheit = 0° Celsius. A function that converts temperatures in Fahrenheit to those in Celsius is
f(x) =
5
9(x – 32) Fahrenheit. Find a formula for the inverse of the function described.
A)
f–1(x) =
5
9(x – 32)
B)
f–1(x) =
9
5x – 32
C)
D)
f–1(x) = x + 32
84)
An organization determines that the cost per person of chartering a bus is given by the formula
C(x) =250 +4x
x,
where x is the number of people in the group and C(x) is in dollars. Find a formula for the inverse of the
function described.
A)
C–1(x) =4
x –250
B)
C–1(x) =250 + x
4
C)
D)
C–1(x) =250
x +4
85)
A size 6 dress in Country C is size 28 in Country D. A function that converts dress sizes in Country C to those in
Country D is f(x) = x +22.Find a formula for the inverse of the function described. Use the inverse function to
find dress sizes in the Country C that correspond to the size of 30 in France.
A)
4
B)
8
C)
D)
1
8
Graph.
86)
f(x) =log 3 x
A)
B)
32
C)
D)
87)
f(x) =log 1/5 x
A)
B)
33
C)
D)
Graph both functions using the same set of axes.
88)
f(x) =2x, f–1(x) =log2 x
A)
B)
34
C)
D)
Convert to a logarithmic equation.
89)
53=125
A)
5= log 3125
B)
3= log 5125
C)
D)
125 = log 53
90)
42=16
A)
2= log 16 4
B)
16 = log 42
C)
D)
4= log 216
91)
5-3 =1
125
A)
-3 = log 51
125
B)
1
125 = log 5-3
C)
D)
-3 = log1/125 5
92)
3431/3=7
A)
1
3=log 343 7
B)
7=log 343
1
3
C)
D)
7=log 1/3343
93)
e4=54.60
A)
e =log 454.60
B)
54.60 =log e4
C)
D)
54.60 =log 4e
Convert to an exponential equation.
94)
log 39=2
A)
23=9
B)
92=3
C)
D)
39=2
95)
log 81
512 =-3
A)
8512 =3
B)
(1
512 )3=8
C)
D)
8-3 =1
512
96)
log 81=0
A)
81=0
B)
80=1
C)
D)
10=8
97)
log wQ =20
A)
Q20 = w
B)
w20 = Q
C)
D)
Qw=20
98)
log 10 10,000,000 =7
A)
10,000,0007= 10
B)
10,000,00010 =7
C)
D)
107=10,000,000
99)
log e3=1.099
A)
3e=1.099
B)
e1.099 =3
C)
D)
31.099 = e
Solve.
100)
log 327 = x
A)
9
B)
81
C)
D)
3
101)
log 2
1
4= x
A)
2
B)
1
2
C)
D)
-2
102)
log 5 x =2
A)
25
B)
32
C)
D)
7
103)
log 5 x =-2
A)
3
B)
1
25
C)
D)
1
32
104)
log 9 1 = x
A)
9
B)
0
C)
D)
81
105)
log x243 =5
A)
5 or -5
B)
3
C)
D)
5
106)
log 5 x = – 3
A)
243
B)
–15
C)
D)
1
125
107)
log 27 x =2
3
A)
27
B)
18
C)
D)
3
108)
log25 x = 0
A)
–1
B)
1
C)
D)
0
109)
log64 x =1
3
A)
16
B)
1
4
C)
D)
4
Find the logarithm.
110)
log51
5
A)
1
B)
0
C)
D)
5
111)
log51
25
A)
2
B)
–2
C)
D)
5
112)
log81
512
A)
3
B)
–64
C)
D)
64
113)
log91
729
A)
–3
B)
81
C)
D)
–81
114)
log8 32
A)
3
2
B)
5
4
C)
D)
5
3
115)
log10 0.01
A)
3
B)
-2
C)
D)
1
116)
log66
A)
6
B)
1
C)
D)
–1
Find the common logarithm to four decimal places.
117)
log 3.546
A)
1.2658
B)
0.0497
C)
D)
1.7658
118)
log 2415
A)
7.7895
B)
2.8829
C)
D)
3.3829
119)
log 68
A)
4.2195
B)
1.8325
C)
D)
1.3325
120)
log 0.82
A)
-0.5862
B)
-0.1985
C)
D)
0.3015
Using a calculator, find to the nearest ten–thousandth.
121)
101.3227
A)
3.7530
B)
0.1215
C)
D)
21.0233
122)
100.3426
A)
-1.0713
B)
-0.4652
C)
D)
1.4086
123)
103.8317
A)
46.1226
B)
6787.3462
C)
D)
1.3434
124)
10-1.0057
A)
95.6961
B)
0.0099
C)
D)
0.0987
125)
10-2.2218
A)
56.0067
B)
0.0006
C)
D)
0.0060
Express as a sum of logarithms.
126)
log 3(225 ·171)
A)
log 3225 +log 3171
B)
log 338,475 +log 338,475
C)
log 225 3+log 171 3
D)
log 33+log 225 225 +log 171 171
127)
log 2(11x)
A)
log 111 –log 1x
B)
log 211 +log 2x
C)
D)
log 211 –log 2x
128)
log 4xy
A)
log 4x +log 4y
B)
log 4x –log 4y
C)
D)
log 2x +log 2y
129)
log r6T
A)
log 6r +log Tr
B)
log r6+log rT
C)
log r6+log rT +log rr
D)
log 6+ log T
130)
log 3(27 ·81)
A)
log 27 3+log 81 3
B)
log 327 +log 381 +log 33
C)
log 33+log 34
D)
log 327 +log 381
Express as a single logarithm.
131)
log 312 +log 311
A)
log 323
B)
log 623
C)
D)
log 6132
132)
log 68+log 66
A)
log 12 14
B)
log 12 48
C)
D)
log 614
133)
log bx +log by
A)
log 2b xy
B)
log b(x + y)
C)
D)
log bxy
39
134)
log cq+log cr
A)
log c
q
r
B)
log cq·log cr
C)
D)
log c(q + r )
135)
log a28 +log a4
A)
log a28
B)
log 2a 32
C)
D)
log a32
Express as a product.
136)
log bt10
A)
10 log bt
B)
10 log bt10
C)
D)
blog 100t10
137)
log 5y4
A)
4log 5y
B)
5log 4y4
C)
D)
4log 5y4
138)
log cZ-2
A)
clog 2Z
B)
-2 log cZ
C)
D)
–clog -2 Z
139)
log 10 x7
A)
7log 10 x
B)
log 70 x
C)
D)
7log 10 x7
140)
log 10 x-4
A)
log -40 x
B)
10 log -4 x
C)
D)
-4 log 10 x-4
Express as a difference of logarithms.
141)
loga11
5
A)
loga11 –loga5
B)
loga11 –5
C)
D)
loga5–11
142)
loguU
6
A)
logu U –6
B)
logu6– U
C)
D)
logu6–logu U