Chapter 10
Chapter
T
es
t
579
Chapter T
es
t
10
10
Find the inv
erse of the function.
1.
f
(
x
)
5
x
8
2.
f
(
x
)
2
√
—
x
+
3
1
3.
f
(
x
)
1
—
3
x
2
+
4,
x
≥
0
Graph the function
f
. Describe the domain and range. Compare the graph of
f
to
thegraph of
g
.
4.
f
(
x
)
√
—
x
+
6
;
g
(
x
)
√
—
x
5.
f
(
x
)
√
—
x
3
+
2;
g
(
x
)
√
—
x
6.
f
(
x
)
3
√
—
x
5;
g
(
x
)
3
√
—
x
7.
f
(
x
)
2
3
√
—
x
+
1
;
g
(
x
)
3
√
—
x
Solve the equation. Check yo
ur solution(s).
8.
9
√
—
x
3
9.
√
—
2
x
7
3
6
10.
√
—
8
x
21
√
—
18
5
x
11.
x
+
5
√
—
7
x
+
53
12.
When solving the equation
x
5
√
—
ax
+
b
, you obtain
x
2 and
x
8. Explain why at
least one of these solutions must be extraneous.
Describe the transfo
rmations from the graph of
f
(
x
)
3
√
—
x
to the graph of the given
function. T
hen graph the given function.
13.
h
(
x
)
4
3
√
—
x
1
+
5
14.
w
(
x
)
3
√
—
x
+
7
2
15.
The velocity
v
(in meters per second) of a roller coaster at the bottom of a hill is giv
en by
v
√
—
19.6
h
, where
h
is the height (in meters) of the hill. (a) Use a graphing calculator to
graph the function. Describe the domain and range. (b) How
tall must the hill be for the
velocity of the roller coaster at the bottom of the hill to be at least 28 meters per second?
(c) W
hat happens to the av
erage rate of change of the v
elocity as the height of the
hill increases?
16.
The speed
s
(in meters per second) of sound through air is giv
en by
s
20
√
—
T
+
273
, where
T
is the temperature (in degrees Celsius).
a.
What is the temperature when the speed of sound through air is
340 meters per second?
b.
How long
does it take you to hear the wolf ho
wl when
the
temperature is
17
°
C?
17.
How can
you restrict the domain of the function
f
(
x
)
(
x
3)
2
so that the in
v
erse of
f
is a function?
18.
Write a radical function that has a domain of all real numbers less than or equal to 0
and a range of all real numbers greater than or equal to 9.
you
wolf
1760 m
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