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# Final_REVIEW - Review Problems MATH 224 Final Fall 2008 1...

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Review Problems MATH 224 Final Fall 2008 1. Be sure to look over all old quizzes, assignments, midterm exam and the midterm review. Approximately 1/3 of the exam will be on material covered before the midterm and 2/3 on material after the midterm. 2. Prove by induction starting at N = 1 , that B(N,1) = N based on the recursive definition given in class. (See PowerPoint slide Recursion.ppt .) 3. Which of the following are one-to-one functions. For the functions that are not one-to-one, provide values of x that confirm this. a. f(x) = 4x 2 + 2x -10 where the domain equals is the set of real numbers. b. f(x) = floor (x) where the domain is the set of integers c. f(x) = 2x, where the domain is the set of real numbers. d. f(x) = 1/x if x ≠ 0, and f(0) = 0, where the domain is the set of all real numbers. e. f(x) = x+1 if x is an odd number, and f(x) = x-1 if x is an even number, where the domain is the set of positive integers. 4. Set S contains N+1 positive integers all less than or equal to 2N . Prove by induction starting at N = 1

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