Find the largest possible subset A of R that will make the following function we

Question

Find the largest possible subset A of R that will make the following function well-defined. f: A rigtharrow R given by f(x) = squareroot 4x - 11 Is the function f: N rigtharrow N given by f(n) = n^2 one to one? Explain, and be specific. Is the function f: Z rigtharrow N given by f(n) = |n| + 2 onto? Explain, and be specific. For f: R rigtharrow R given by f(x) = 11x + 7, find the inverse, f^-1 (x). Let R be a relation from A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} to B = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10} given by R = {(a, b) | 2a

Explanation / Answer

14) R = { (1,3), (1, 4), (1,5), (1,6), (1,7), (1,8), (1,9), (1,10), (2,5), (2,6), (2,7), (2,8), (2,9), (2,10), (3,7), (3,8), (3,9), (3,10), (4,9), (4,10)}

15) a) No, R is not not reflexive. Because (1,1) cannot be in R.

b) Yes, R is symetric. Because for every (x,y), there will be (y,x). for example for (1,2), there is also (2,1).

C) No, R is not transitive. Because for (1,3), (3,1), there is not (1,1).

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