quiz 16A sol - Solutions to Quiz 16A...

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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 x-2 1-x + 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.

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quiz 16A sol - Solutions to Quiz 16A...

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