47 / 84
Check Your Understanding
=
Step-by-Step Solutions begin on page R14.
Find the inverse of each relation.
1.
{
(
-
9, 10), (1,
-
3), (8,
-
5)
}
2.
{
(
-
2, 9), (4,
-
1), (
-
7, 9), (7, 0)
}
Find the inverse of each function. Then graph the function and its inverse.
3.
f
(
x
)
= -
3
x
4.
g
(
x
)
=
4
x
-
6
5.
h
(
x
)
=
x
2
-
3
Find the inverse for each function. Then graph the function and its inverse. If necessary,
restrict the domain of
f
(
x
) so that the inverse is a function.
6.
f
(
x
)
=
x
2
+
4
x
-
5
7.
f
(
x
)
=
x
2
-
16
x
+
63
Determine whether each pair of functions are inverse functions. Write
yes
or
no
.
8.
f
(
x
)
=
x
-
7
9.
f
(
x
)
=
1
_
2
x
+
3
_
4
10.
f
(
x
)
=
2
x
3
g
(
x
)
=
x
+
7
g
(
x
)
=
2
x
-
4
_
3
g
(
x
)
=
1
_
3
√
x
Practice and Problem Solving
Extra Practice is on page R5.
Find the inverse of each relation.
11.
{
(
-
8, 6), (6,
-
2), (7,
-
3)
}
12.
{
(7, 7), (4, 9), (3,
-
7)
}
13.
{
(8,
-
1), (
-
8,
-
1), (
-
2,
-
8), (2, 8)
}
14.
{
(4, 3), (
-
4,
-
4), (
-
3,
-
5), (5, 2)
}
SENSE-MAKING
Find the inverse of each function. Then graph the function
and its inverse.
15.
f
(
x
)
=
x
+
2
16.
g
(
x
)
=
5
x
17.
f
(
x
)
= -
2
x
+
1
18.
h
(
x
)
=
x
-
4
_
3
19.
f
(
x
)
= -
5
_
3
x
-
8
20.
g
(
x
)
=
x
+
4
21.
h
(
x
)
=
x
2
+
4
22.
f
(
x
)
=
1
_
2
x
2
-
1
23.
f
(
x
)
=
(
x
+
1)
2
+
3
Find the inverse for each function. Then graph the function and its inverse. If necessary, restrict
the domain of
f
(
x
) so that the inverse is a function.
24.
f
(
x
)
=
4
x
25.
f
(
x
)
= -
8
x
+
9
26.
f
(
x
)
=
5
x
2
27.
f
(
x
)
=
x
2
+
12
x
+
32
28.
f
(
x
)
=
x
2
-
22
x
+
120
29.
f
(
x
)
=
x
2
-
36
x
-
160
Determine whether each pair of functions are inverse functions. Write
yes
or
no
.
30.
f
(
x
)
=
2
x
+
3
31.
f
(
x
)
=
4
x
+
6
32.
f
(
x
)
= -
1
_
3
x
+
3
g
(
x
)
=
2
x
-
3
g
(
x
)
=
x
-
6
_
4
g
(
x
)
= -
3
x
+
9
33.
f
(
x
)
= -
6
x
34.
f
(
x
)
=
1
_
2
x
+
5
35.
f
(
x
)
=
x
+
10
_
8
g
(
x
)
=
1
_
6
x
g
(
x
)
=
2
x
-
10
g
(
x
)
=
8
x
-
10
36.
f
(
x
)
=
2
_
3
x
3
f
(
x
)
=
(
x
+
6)
2
38.
f
(
x
)
=
2
√
x
-
5
g
(
x
)
=
√
2
_
3
x
g
(
x
)
=
√
x
-
6
g
(
x
)
=
1
_
4
x
2
-
5
39.
FUEL
The average miles traveled for every gallon
g
89
PREMIUM
87
REGULAR
PricePerGallon
Purchase
Gallons
of gas consumed by Leroy’s car is represented by
the function
m
(
g
)
=
28
g
.
a.
Find a function
c
(
g
) to represent the cost per
gallon of gasoline.
b.
Use inverses to determine the function used
to represent the cost per mile traveled in
Leroy’s car.
Example 1
Example 2
Example 3
Example 4
Example 1
Example 2
Example 3
Example 4
37
for a
Self-Check Quiz
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