Homework: Section 10.2
Math 112 (Spring 2013)
Graded Problems
The answers to these problems will be graded for accuracy; no partial credit will be given. Leave all answers
in exact form (i.e. no decimal approximations) unless specifically asked to round. In order to
make the grading easier, please turn in a single sheet of paper containing only your answers. Remember that
you can check your answers with me before you turn in the assignment.
1. (1pt) Is the function f (x) =
2
2x+3
invertible? If so, find its inverse.
2. (1pt) Is the function g(x) = 3x − 1 invertible? If so, find its inverse.
3. (1pt) Is the function h(x) = |2x + 3| − 1 invertible? If so, find its inverse.
4. (1pt) Is the function p(x) = 2 log(x) + 3 invertible? If so, find its inverse.
q
5. (1pt) True or False: The functions f (x) = 1 + 7x3 and g(x) = 3 x−1
7 inverses of each other.
6. (1pt) True or False: The functions f (x) = 1 −
1
x−1
and g(x) = 1 +
1
1−x
inverses of each other.
7. (1pt) Find any two functions f and g such that (f ◦ g)(x) = x for all x but there exists a number t
such that (g ◦ f )(t) 6= t.
8. (2pt) The airspeed velocity of a European swallow is proportional to its heart rate. That is, if a
European swallow’s heart rate is h beats per minute then its airspeed is A(h) = 0.01h meters per
second.
(a) The average heart beat of a European swallow is 900 beats per minute. What is the airspeed
velocity of such a swallow?
(b) If a European swallow flies at 11.5 meters per second, find its heart rate.
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9. (1pt) Sketch the inverse of the function graphed below:
y
6
5
4
3
2
1
x
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
Non-graded Practice Problems
These problems will not be graded; instead they are simply meant to be extra practice for those who desire it.
Please do not include these problems in the assignment that you turn in for grading.
• Book Problems: 1-6 (use wolfram alpha or a graphing calculator to graph these), 7-37, 40-44, 47-51,
55-64
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