This preview shows pages 1–2. Sign up to view the full content.
Exercises
UF Calculus Set 5
1. Determine whether the following represent onetoone functions:
(a) a rule that associates a person with his/her nuclear DNA
(b) a rule that associates a person with his/her current set of ﬁngerprints
(c) a rule that associates, to a given time, the distance from a swinging pendulum to its
lowest point
(d) a rule that associates, to a given distance traveled, the speed of an object falling from a
building without air resistence
2. The function
f
(
x
) =
x
+
e
x

1
is onetoone. By inspection, what is
f

1
(0)
? what is
f

1
(
e
)
?
3. A tank continuously drains so that the volume
V
of water (in gallons) remaining in the tank
after
t
minutes is
V
(
t
) = 100(1

t
20
)
2
.
(a) What is the domain of
V
(
t
)
by the context of the problem? What is the range?
(b) What is implied about the physical nature of the problem that ensures
V
(
t
)
is onetoone
on its domain? Find the inverse function.
(c) What is
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 ALL
 Calculus, Geometry

Click to edit the document details