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Check Your Understanding
=
Step-by-Step Solutions begin on page R14.
Given
f
(
x
)
=
x
2
+
3 and
g
(
x
)
=
2
x
−
10, find each value.
1.
[
f
◦
g
](4)
2.
[
g
◦
f
](4)
3.
[
f
◦
g
](0)
4.
[
g
◦
f
](0)
5.
[
f
◦
g
](−1)
6.
[
g
◦
f
](
−
1)
7.
[
f
◦
g
](5)
8.
[
f
◦
g
](
−
4)
9.
[
g
◦
f
](2)
For each pair of functions, find
f
◦
g
and
g
◦
f
, if they exist. State the domain
and range for each composed function.
10.
f
=
{(2, 5), (6, 10), (12, 9), (7, 6)}
11.
f
=
{(
−
5, 4), (14, 8), (12, 1), (0,
−
3)}
g
=
{(9, 11), (6, 15), (10, 13), (5, 8)}
g
=
{(
−
2,
−
4), (
−
3, 2), (
−
1, 4), (5,
−
6)}
Find [
f
◦
g
](
x
) and [
g
◦
f
](
x
), if they exist. State the domain and range for each
composed function.
12.
f
(
x
)
= −
3
x
13.
f
(
x
)
=
x
+
4
g
(
x
)
=
5
x
−
6
g
(
x
)
=
x
2
+
3
x
−
10
14.
MODELING
Dora has 8% of her earnings deducted from her paycheck for
a college savings plan. She can choose to take the deduction either before taxes are
withheld, which reduces her taxable income, or after taxes are withheld. Dora’s tax
rate is 17.5%. If her pay before taxes and deductions is $950, will she save more money
if the deductions are taken before or after taxes are withheld? Explain.
Practice and Problem Solving
Extra Practice is on page R5.
Given
f
(
x
)
=
x
+
4,
g
(
x
)
= −
2
x
2
, and
h
(
x
)
=
5, find each value.
[
f
◦
g
](10)
16.
[
g
◦
f
](10)
17.
[
f
◦
h
](0)
18.
[
h
◦
f
](3)
19.
[
g
◦
h
](−
2
)
20.
[
h
◦
g
](
−
2)
21.
[
f
◦
g
](
−
4)
22.
[
g
◦
f
](
−
4)
23.
[
g
◦
f
](
−1
2)
For each pair of functions, find
f
◦
g
and
g
◦
f
, if they exist. State the domain and range
for each composed function.
24.
f
=
{(
−
8,
−
4), (0, 4), (2, 6), (
−
6,
−
2)}
25.
f
=
{(
−
7, 0), (4, 5), (8, 12), (
−
3, 6)}
g
=
{(4,
−
4), (
−
2,
−
1), (
−
4, 0), (6,
−
5)}
g
=
{(6, 8), (
−
12,
−
5), (0, 5), (5, 1)}
26.
f
=
{(5, 13), (
−
4,
−
2), (
−
8,
−
11), (3, 1)}
27.
f
=
{(
−
4,
−
14), (0,
−
6), (
−
6,
−
18), (2,
−
2)}
g
=
{(
−
8, 2), (
−
4, 1), (3,
−
3), (5, 7)}
g
=
{(
−
6, 1), (
−
18, 13), (
−
14, 9), (
−
2,
−
3)}
28.
f
=
{(
−
15,
−
5), (
−
4, 12), (1, 7), (3, 9)}
29.
f
=
{(
−
1, 11), (2,
−
2), (5,
−
7), (4,
−
4)}
g
=
{(3,
−
9), (7, 2), (8,
−
6), (12, 0)}
g
=
{(5,
−
4), (4,
−
3), (
−
1, 2), (2, 3)}
30.
f
=
{(7,
−
3), (
−
10,
−
3), (
−
7,
−
8), (
−
3, 6)}
31.
f
=
{(1,
−
1), (2,
−
2), (3,
−
3), (4,
−
4)}
g
=
{(4,
−
3), (3,
−
7), (9, 8), (
−
4,
−
4)}
g
=
{(1,
−
4), (2,
−
3), (3,
−
2), (4,
−
1)}
32.
f
=
{(
−
4,
−
1), (
−
2, 6), (
−
1, 10), (4, 11)}
33.
f
=
{(12,
−
3), (9,
−
2), (8,
−
1), (6, 3)}
g
=
{(
−
1, 5), (3,
−
4), (6, 4), (10, 8)}
g
=
{(
−
1, 5), (
−
2, 6), (
−
3,
−
1), (
−
4, 8)}
Example 2
Example 3
Example 1
15
Example 2
for a
Self-Check Quiz
Example 1
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