ONLY DO PROBLEMS (B) - (J)

THEORY FOUNDATION SUBJECT***

Exercise 3.4.2: Finding inverses of functions. 0 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 (a) f: ZZ. f(x) = x +3 (b) f:Z + Z. f(x) = 2x + 34 f:R R. f(x) = 2.c + 3 (d) Let A be defined to be the set {1,2,3,4,5,6,7,8} f:P(A) {0,1,2,3,4,5,6,7,8} For X C A f(x) = [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. Let A be defined to be the set {1,2,3,4,5,6,7,8}. f: P(A) + P(A). For X CA, 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. (1) f:{0,1}} + {0,1}3. 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. (9) 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}} + {0,1}3. The output of f is obtained by taking the input string x, removing the first bit of c, and adding the bit to the end of x. For example, f(011) = 110. 0 f:Zx Z Z Z f(x,y) = (x + 5,4 - 2)