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Exercise 3.4.2: Finding inverses of functions. i About For each of the following functions, indicate whether the function has a well-defined inverse. If the inverse is well-defined, give the input/output relationship of f-1 Let A be defined to be the set {1,2,3,4,5,6,7,8}. f : P(A) + P(A). For X C A, f(X) = A X. Recall that for a finite set A, P(A) denotes the power set of A which is the set of all subsets of A. (9) f: {0, 1}} + {0,1}. The output of f is obtained by taking the input string and replacing the first bit by 1, regardless of whether the first bit is a 0 or 1. For example, f(001) = 101 and f(110) = 110. (g) f : {0, 1}} + {0,1}3. The output of f is obtained by taking the input string and reversing the bits. For example, f(011) = 110 (h) f:{0,1}3 + {0,1}. The output of f is obtained by taking the input string x, removing the first bit of , and adding the bit to the end of x. For example, f(011) = 110. 0 f: Z Z+ZxZ, f(x, y) = (x +5,4 2) 0 f: Z Z+Zx Z, f(x, y) = (1 y,x)