76 / 84
CHAPTER 5
Study Guide and Review
Continued
Find [
f
◦
g
](
x
) and [
g
◦
f
](
x
).
17.
f
(
x
)
=
2
x
+
1
18.
f
(
x
)
=
x
2
+
1
g
(
x
)
=
4
x
-
5
g
(
x
)
=
x
-
7
19.
f
(
x
)
=
x
2
+
4
20.
f
(
x
)
=
4
x
g
(
x
)
= -
2
x
+
1
g
(
x
)
=
5
x
-
1
21.
f
(
x
)
=
x
3
22.
f
(
x
)
=
x
2
+
2
x
-
3
g
(
x
)
=
x
-
1
g
(
x
)
=
x
+
1
23.
MEASUREMENT
The formula
f
=
3
y
converts yards
y
to feet
f
and
f
=
n
_
12
converts inches
n
to feet
f
. Write
a composition of functions that converts yards to inches.
Example 2
If
f
(
x
)
=
x
2
+
3 and
g
(
x
)
=
3
x
-
2, find
g
[
f
(
x
)]
and
f
[
g
(
x
)].
g
[
f
(
x
)]
=
3(
x
2
+
3)
-
2
Replace
f
(
x
) with
x
2
+
3.
=
3
x
2
+
9
-
2
Distributive Property
=
3
x
2
+
7
Simplify.
f
[
g
(
x
)]
=
(3
x
-
2)
2
+
3
Replace
g
(
x
) with 3
x
-
2.
=
9
x
2
-
12
x
+
4
+
3
Multiply.
=
9
x
2
-
12
x
+
7
Simplify.
Given
f
(
x
)
=
2
x
+
9 and
g
(
x
)
=
x
2
+
2
x
+
1, find each function.
9.
(
f
+
g
)(
x
)
10.
(
f
–
g
)(
x
)
11.
(
f
·
g
)(
x
)
12.
(
f
_
g
)
(
x
)
Given
f
(
x
)
=
10
x
and
g
(
x
)
=
x
3
–
8, find each function.
13.
(
f
+
g
)(
x
)
14.
(
f
–
g
)(
x
)
15.
(
f
·
g
)(
x
)
16.
(
f
_
g
)
(
x
)
Example 2
Given
f
(
x
)
=
3
x
+
1 and
g
(
x
)
=
x
3
+
1, find each function.
a.
(
f
–
g
)(
x
)
(
x
-
g
)(
x
)
=
f
(
x
)
-
g
(
x
)
Subtraction of functions
=
(3
x
+
1)
-
(
x
3
+
1)
Substitution
=
3
x
-
x
3
Simplify.
b.
(
f
_
g
)
(
x
)
(
f
_
g
)
(
x
)
=
f
(
x
)
_
g
(
x
)
Division of functions
=
(3
x
+
1)
_
(
x
3
+
1)
Substitution
Lesson-by-Lesson Review
5-2
Composition of Functions
5-1
Operations with Functions
Find the inverse of each function. Then graph the function
and its inverse.
24.
f
(
x
)
=
5
x
-
6
25.
f
(
x
)
= -
3
x
-
5
26.
f
(
x
)
=
1
_
2
x
+
3
27.
f
(
x
)
=
4
x
+
1
_
5
28.
f
(
x
)
=
x
2
29.
f
(
x
)
=
(2
x
+
1)
2
30.
SHOPPING
Samuel bought a computer. The sales tax
rate was 6% of the sale price, and he paid $50 for
shipping. Find the sale price if Samuel paid a total
of $1322.
Example 3
Find the inverse of
f
(
x
)
= -
2
x
+
7.
Rewrite
f
(
x
) as
y
= -
2
x
+
7. Then interchange the variables
and solve for
y
.
x
= -
2
y
+
7
Interchange the variables.
2
y
= -
x
+
7
Solve for
y
.
y
=
-
x
+
7
_
2
Divide each side by 2.
f
-
1
(
x
)
=
-
x
+
7
_
2
Rewrite using function notation.
5-3
Inverse Functions and Relations
362
|
Chapter 5
|
Study Guide and Review