Discrete Mathematical Structures by Pearson

Functions 3-3

Example 2 Let f: N → N be a function defined by f (x) = x + 2, for all x ∈ N. Prove that f is a

function. Find domain, co-domain and range of f.

Solution: f is a function since every natural number is assigned to a unique natural number

which is obtained by adding 2 to the number.

For example, f (1) = 1 + 2 = 3, f (2) = 2 + 2 = 4, f (3) = 3 + 2 = 5, and so on.

Domain = N, Co-domain = N, Range = N - {1, 2}.

Example 3 Let f: A → A be defined by f = {(1, 3), (2, 3), (3, 1), (4, 4)}, where A = {1, 2, 3, 4}.

Find domain, co-domain, and range of the function f.

Solution: Since each element of set A is assigned a unique element in co-domain ...