Exam 2 Pre Calculus I
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Section: 016 Date: 03/20/2015
Use this result to find what is g(x) if (f ◦ g)(x) =
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Q 1. Simplify f −1 ◦ (f ◦ g)(x).
3x2 + 1 and f (x) = x + 1
1
2
Dr. Petrescu CCP MATH161 Exam 2 A
x+2
2x − 1
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Q 2. Find h−1 (x) if h(x) =
Dr. Petrescu CCP MATH161 Exam 2 A
x3 + 1
a) f (x) = √
x2 + 1
√
3
z2 + 1
b) g(z)= 3
z +1
4x2 + 9x + 2
x2 + 4x + 4
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c) y(x) =
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Q 3. Find the domain of the following functions:
3
4
Dr. Petrescu CCP MATH161 Exam 2 A
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Q 4. In a certain state the maximum speed permitted on freeways is 75 mi/ h, and
the minimum is 40 mi/h. The fine F for violating these limits is $9.00 for every
mile above the maximum or below the minimum. Complete the expressions in the
following piecewise defined function, where x is the speed at which you are driving.

if 0 ≤ x < 40

if 40 ≤ x ≤ 75
f (x) =

if 75 < x
Dr. Petrescu CCP MATH161 Exam 2 A
5
Q 5. Graph the function :
if − ∞ ≤ x ≤ 0
if 0 < x < 2
if 2 < x
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
1

 1− x
2
h(x) =
2x + 1


|x|
6
Dr. Petrescu CCP MATH161 Exam 2 A
Q 6. Decide if the graphs below are graphs of a function. If they are decide whether
or not the function is invertible (i.e. f (x) has an inverse):
y
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y
x
a.
b.
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y
x
c.
x
Dr. Petrescu CCP MATH161 Exam 2 A
7
Q 7. Given the function z(x) below, sketch the graphs of
z(x − 1)
b. z(−(x + 1))
c. 2 z(−2x)
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Make sure you clearly mark all points in your sketches.
z(x)
−1.35
1.35
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−2
x
Dr. Petrescu CCP MATH161 Exam 2 A
Q
a.
b.
c.
d.
e.
8. For the function in question 7
Find where it is decreasing.
Find where it is increasing
Find the average rate of change between x = −1.35 and x = 1.35
Find the average rate of change between x = −1.35 and x = 0
Find the average rate of change between x = 0 and x = 1.35
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8
Dr. Petrescu CCP MATH161 Exam 2 A
Q 9. If f (x) =
9
1
, find:
x−3
b. f −1 ◦ f (x) and its domain.
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a. f −1 and its domain
10 Dr. Petrescu CCP MATH161 Exam 2 A
Q 10. If f (x) =
1
and g(x) = x2 + 1, find:
x+2
b. g ◦ f (x) and its domain.
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a. f ◦ g(x) and its domain