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problems04-sol - MATH S-104 Lecture 4 In-class Problem...

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MATH S-104 Lecture 4 In-class Problem Solutions July 2, 2009 Problem 1 : Let X = { 1 , 3 , 5 } and Y = { a,b,c,d } . Draw an arrow diagram that defines a function f with each of the following characteristics, or explain why such a function cannot exist. a) f is not a well-defined function. a b c 1 3 5 d a b c 1 3 5 d The arrow diagram on the left is not well-defined because 3 has no image in Y . The diagram on the right is not a well-defined function because 1 is mapped to multiple images in Y . b) f is not a well-defined function, but f - 1 is. a b c 1 3 5 d a b c 1 3 5 d c) f is a function that is one-to-one but not onto. a b c 1 3 5 d f is not onto because b has no preimage in X . d) f is a function and f - 1 is a function. Such a function is not possible with the specified domain and codomain, because Y X . 1
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Problem 2 * : Find at least three di ff erent sequences beginning with the terms 1,2,4 whose terms are generated by a simple formula. Some correct answers are: a n = 2 n , n = 0 , 1 , 2 ,...
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