Answer
a)Domain is Z+ x Z+; Range is Z+ .
b)Domain is Z+ ; Range is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
c)Domain is the set of bit strings;Range is N.
d)Domain is the set of bit strings;Range is N.
Work Step by Step
In each case, the domain is the set of possible inputs for which the function is defined, and the range is the set of all possible outputs on these inputs.
a) The domain is Z+ x Z+, since we are told that the function operates on pairs of positive integers (the word "pair" in mathematics is usually understood to mean ordered pair). Since the maximum is again a positive integer, and all positive integers are possible maximums (by letting the two elements of the pair be the same),
the range is Z+ .
b) We are told that the domain is Z+ . Since the decimal representation of an integer has to have at least one digit, at most nine digits do not appear, and of course the number of missing digits could be any number less than 9. Thus the range is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
c) We are told that the domain is the set of bit strings. The block 11 could appear no times, or it could appear any positive number of times, so the range is N.
d) We are told that the domain is the set of bit strings. Since the first 1 can be anywhere in the string, its position can be 1, 2, 3, .... If the bit string contains no 1's, the value is 0 by definition. Therefore the range
is N.
