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CHAPTER 5
Mid-Chapter Quiz
Lessons 5-1 through 5-3
Given
f
(
x
)
=
2
x
2
+
4
x
-
3 and
g
(
x
)
=
5
x
-
2, find
each function.
(Lesson 5-1)
1.
(
f
+
g
)(
x
)
2.
(
f
-
g
)(
x
)
3.
(
f
·
g
)(
x
)
4.
(
f
_
g
)
(
x
)
5.
FINANCE
A small company is producing a new
product. The revenue
r
(
x
) from the sale of
x
units of
the new product is expected to be
r
(
x
)
=
10
x
. The
cost of manufacturing
x
units is
c
(
x
)
=
2.25
x
+
2000.
(Lesson 5-1)
a.
Write the profit function.
b.
Find the profit on 1000 units of the product.
c.
What mathematical practice did you use to
solve this problem?
Given
f
(
x
)
=
2
x
2
+
4
x
-
3 and
g
(
x
)
=
5
x
-
2, find each
function.
(Lesson 5-2)
6.
[
f
◦
g
](
x
)
7.
[
g
◦
f
](
x
)
8.
PRODUCTION
The cost in dollars of producing
p
cell
phones in a factory is represented by
C
(
p
)
=
5
p
+
60. The number of cell phones produced in
h
hours
is represented by
P
(
h
)
=
40
h
.
(Lesson 5-2)
a.
Find the composition function.
b.
Determine the cost of producing cell phones for
8 hours.
Find [
f
◦
g
](
x
) and [
g
◦
f
](
x
), if they exist. State the domain
and range for each composed function.
(Lesson 5-2)
9.
f
(
x
)
=
4
x
g
(
x
)
=
x
-
8
10.
f
(
x
)
=
3
x
-
1
g
(
x
)
=
5
x
+
1
11.
f
(
x
)
= -
2
x
g
(
x
)
=
x
2
-
8
12.
SHOPPING
Mrs. Ross is shopping for her children’s
school clothes. She has a coupon for 25% off her
total. The sales tax of 6% is added to the total after
the coupon is applied.
(Lesson 5-2)
a.
Express the total price after the discount and the
total price after the tax using function notation. Let
x
represent the price of the clothing,
p
(
x
) represent
the price after the 25% discount, and
g
(
x
) represent
the price after the tax is added.
b.
Which composition of functions represents the
final price,
p
[
g
(
x
)] or
g
[
p
(
x
)]? Explain your
reasoning.
Determine whether each pair of functions are inverse
functions. Write
yes
or
no
.
(Lesson 5-3)
13.
f
(
x
)
=
2
x
+
16
14.
g
(
x
)
=
4
x
+
15
g
(
x
)
=
1
_
2
x
-
8
h
(
x
)
=
1
_
4
x
-
15
15.
f
(
x
)
=
x
2
-
5
16.
g
(
x
)
= -
6
x
+
8
g
(
x
)
=
5
+
x
-
2
h
(
x
)
=
8
-
x
_
6
Find the inverse of each function, if it exists.
(Lesson 5-3)
17.
h
(
x
)
=
2
_
5
x
+
8
18.
f
(
x
)
=
4
_
9
(
x
-
3)
19.
h
(
x
)
= -
10
_
3
(
x
+
5)
20.
f
(
x
)
=
x
+
12
_
7
Use the horizontal line test to determine whether the
inverse of each function is also a function.
(Lesson 5-3)
21.
f
(
x
)
=
4
x
-
1
22.
f
(
x
)
=
10
x
2
23.
f
(
x
)
=
3
x
3
-
8
24.
JOBS
Louise runs a lawn care service. She charges
$25 for supplies plus $15 per hour. The function
f
(
h
)
=
15
h
+
25 gives the cost
f
(
h
) for
h
hours of
work.
(Lesson 5-3)
a.
Find
f
-
1
(
h
). What is the significance of
f
-
1
(
h
)?
b.
If Louise charges a customer $85, how many
hours did she work?
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