Textbook pp. 146 - 147
2 (b) It is a function
(c) It is not a function because f(-2) and f(2) are not defined.
4 (a) Domain: The set of natural numbers Range: {0, 1, ..., 9}
(c) Doamin: The set of binary numbers Range: The set of natural numbers
12 (c) one-to-one
(d) Not one-to-one because for example f(1) = f(2) = 1.
16 (a) f(x) = x2
(c) f(x) = x + 1 if x is even and f(x) = x - 1 if x is odd.
18 (a) Bijection
(b) Not a bijection
28 (a) The set of even numbers
Textbook pp. 191 - 192
2 (a) It is O(x2).
(c) It is O(x2).
(e) It is not O(x2).
8 (a) n = 4.
14 (c) Yes, x3 is O(x2 + x3).
(d) Yes, x3 is O(x2 + x4).
(e) Yes, x3 is O(3x).
20 (b) 6n (= 2n3n)
(c) nnn!