40 / 84
Find [
f
◦
g
](
x
) and [
g
◦
f
](
x
), if they exist. State the domain and range for each
composed function.
34.
f
(
x
)
=
2
x
f
(
x
)
= −
3
x
36.
f
(
x
)
=
x
+
5
g
(
x
)
=
x
+
5
g
(
x
)
= −
x
+
8
g
(
x
)
=
3
x
−
7
37.
f
(
x
)
=
x
−
4
38.
f
(
x
)
=
x
2
+
6
x
−
2
39.
f
(
x
)
=
2
x
2
−
x
+
1
g
(
x
)
=
x
2
−
10
g
(
x
)
=
x
−
6
g
(
x
)
=
4
x
+
3
40.
f
(
x
)
=
4
x
−
1
41.
f
(
x
)
=
x
2
+
3
x
+
1
42.
f
(
x
)
=
2
x
2
g
(
x
)
=
x
3
+
2
g
(
x
)
=
x
2
g
(
x
)
=
8
x
2
+
3
x
43.
SENSE-MAKING
Ms. Smith wants to buy a home theater system, which is on sale
for 35% off the original price of $2299. The sales tax is 6.25%.
a.
Write two functions representing the price after the discount
p
(
x
) and the price after
sales tax
t
(
x
).
b.
Which composition of functions represents the price of the home theater system,
[
p
◦
t
](
x
) or [
t
◦
p
](
x
)? Explain your reasoning.
c.
How much will Ms. Smith pay for the home theater system?
If
f
(
x
)
=
5
x
,
g
(
x
)
= −
2
x
+
1, and
h
(
x
)
=
x
2
+
6
x
+
8, find each value.
44.
f
[
g
(3
a
)]
45.
f
[
h
(
a
+
4)]
46.
g
[
f
(
a
2
−
a
)]
Use the table to find each value.
47.
[
f
◦
g
](
−
2)
48.
[
g
◦
f
](
−
2)
49.
[
f
◦
g
](
−
1)
50.
[
g
◦
f
](1)
51.
[
h
◦
g
](2)
52.
[
g
◦
h
](2)
53.
[
f
◦
h
](0)
54.
[
f
◦
g
](
−
1)
Use the graph of
f
(
x
) and
g
(
x
) to find each value.
55.
[
g
◦
f
](1)
56.
[
f
◦
g
](
−
2)
C05_007A_903990
y
x
O
g
(
x
)
f
(
x
)
C05_008A_903990
y
x
O
f
(
x
)
g
(
x
)
57.
[
f
◦
g
](2)
58.
[
g
◦
f
](1)
C05_009A_903990
y
x
O
f
(
x
)
g
(
x
)
C05_010A_903990
y
x
O
g
(
x
)
f
(
x
)
35
Example 3
x
f
(
x
)
g
(
x
)
h
(
x
)
−
2
−
2
1
0
−
1
−
4
1
0
0
−
2
−
2
−
2
1
2
−
1
−
2
2
−
1
0
5
326
|
Lesson 5-2
|
Composition of Functions