Kenneth Rosen Edition 7 Exercise 2.3 Question 5 (Page No. 152)

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.

1. the function that assigns to each bit string the number of ones in the string minus the number of zeros in the string
2. the function that assigns to each bit string twice the number of zeros in that string
3. the function that assigns the number of bits left over when a bit string is split into bytes (which are blocks of 8 bits)
4. the function that assigns to each positive integer the largest perfect square not exceeding this integer