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Unformatted text preview: Solutions to Quiz 16A
www.math.uﬂ.edu/˜harringt
November 26, 2007
1. Use the chart to answer the following questions.
x
0123
f(x) 1 0 3 2
g(x) 3 1 0 2
(a) (f ◦ g )(2) = f (g (2)) = f (0) = 1
(b) (g ◦ f )(2) = g (f (2)) = g (3) = 2
(c) (g ◦ g )(3) = g (g (3)) = g (2) = 0
2. Please ﬁnd two functions f and g such that (f ◦ g )(x) = √1
.
x2 +1 I would like to point out that the solution is NOT unique, meaning
there are diﬀerent answers one could give and still be correct.
One possible solution:
1
Let f (x) = √x and g (x) = x2 + 1
Another possible solution:√
1
Let f (x) = x and g (x) = x2 + 1
Other solutions may exists. The only solutions that will not be accepted
are the trivial solutions, where either f (x) = x or g (x) = x. Those will
NOT counted as correct.
3. Find the interval for which
(x + 3)(x − 2)
≥0
x(1 − x)
1 We will use a sign chart. Let f (x) = (x+3)(x−2) . For ease of notation,
x(1−x)
we will use # to denote ”undeﬁned” or ”division by zero” within the
chart.
x+3 x2 1x +
x
f(x)  0+++++++
0+
++++#   #+++++
0+##+0 3
0
1
2 From the sign chart, we see that the interval is: [−3, 0) ∪ (1, 2]. 2 ...
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This note was uploaded on 07/12/2011 for the course MAC 1140 taught by Professor Williamson during the Fall '08 term at University of Florida.
 Fall '08
 WILLIAMSON
 Math, Calculus, Algebra

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