Discrete Mathematical Structures by Pearson

3-18 Discrete Mathematical Structures

Solution:

(1) f is a function, since each element of A is associated with a unique element of B.

Range ( f ) = {1, 2, 3, 4}

(2) g is a function, since each element of A is associated with unique element of B.

Range (g) = {1, 3, 4}

(3) h is not a function, since d ∈ A is not associated with any element in B.

Example 2 Find the range of the function f: A → R defined by f (x) = x

2

+ 5, where A = {0, 1, 2, 3}.

Solution: The range of f consists of those elements of R which are f-image of different

elements of A. Now, f (0) = 5, f (1) = 1 + 5 = 6, f (2) = 4 + 5 = 9, f (3) = 14. Thus, the range of

f = {5, 6, 9, 14}.

3.10 ACKERMANN’S FUNCTION

A popular example of a recursive function is Ackermann’s function. ...