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q6-functions - Domain bit strings Range the set of integers...

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CSE 260 QUIZ-6– Functions- ANSWERS (25 minutes) NAME: 1. (10 points) Determine whether f is a function from Z ¯ to R ¯ if (a) f ( n ) = n 2 + 1 This is a function. For all integers n, n 2 + 1 is a well-defined real number. (b) f ( n ) = 1 / ( n 2 - 4) No, f(2) is not defined. 2. (10 points) Find the domain and range of these functions. (a) the function that assigns to each pair of positive integers the first integer of the pair. Domain: Z + × Z + Range: Z + (b) the function that assigns to a bit string the difference between the number of ones and the number of zeros in the string.
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Unformatted text preview: Domain: bit strings Range: the set of integers 3. (10 points) Determine if each of these following functions is a bijection from R ¯ to R ¯ . (a) f ( x ) = 2 x + 1 yes (b) f ( x ) = x 2 + 1 No; f(2)=5, f(-2)=5 4. (10 points) Find the inverse of the function f ( x ) = ax + b from R ¯ to R ¯ , where a and b are constants, with a 6 = 0. Show that it is an inverse. Problem 31 on page 109. Answer on page S-11 of the text book. 1...
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