Answer to Question #269207 in Discrete Mathematics for madiha

Question

Find the domain and range of these functions. Note that in each case, to find the domain, determine the set of elements assigned values by the function. a) the function that assigns to each bit string the number of ones in the string minus the number of zeros in the string b) the function that assigns to each bit string twice the number of zeros in that string c) the function that assigns the number of bits left over when a bit string is split into bytes (which are blocks of 8 bits) d) the function that assigns to each positive integer the largest perfect square not exceeding this integer 

Answer 1

Domain is the set of values that argument might take. Range is the set of values that function might take.

(a) This is the function has two arguments, one for the number of ones and another for the number of zeros, which can be any non-negative integer, so domain is $N∪$ {0} . The range of this function is the set of integers.

(b) The argument of that function is the number zeros in the string, which means the domain of that function is $N∪$ {0}. The range of that function is the set of non-negative even integers

(c) The domain of that function is {1, 2, 3, 4, 5, 6, 7, 8}, the range is {0, 1, 2, 3, 4, 5, 6, 7}

{d) The domain of that function is N, the range is the set {$x|x=n^2, n \in N$}