Answer
a)
Domain: {1,2,3...}
Range: {1,2,3...}
b)
Domain: {1,2,3...}
Range: {0,1,2,3,4,5,6,7,8,9}
c)
Domain: U{0,1} * d, where d is the length of the bit string
Range: {z,...}
d)
Domain: {1,2,3...}
Range: {z,...}
e)
Domain: U{0,1} * d, where d is the length of the bit string
Range: {0,1,2,...}
Work Step by Step
a) the function that assigns to each pair of positive integers the first integer of the pair
Domain: {1,2,3...}
Range: {1,2,3...}
b) the function that assigns to each positive integer its largest decimal digit
Domain: {1,2,3...}
Range: {0,1,2,3,4,5,6,7,8,9}
c) the function that assigns to a bit string the number of ones minus the number of zeros in the string
Domain: U{0,1} * d, where d is the length of the bit string
Range: {z,...}
d) the function that assigns to each positive integer the largest integer not exceeding the square root of the integer
Domain: {1,2,3...}
Range: {z,...}
e) the function that assigns to a bit string the longest string of ones in the string
Domain: U{0,1} * d, where d is the length of the bit string
Range: {0,1,2,...}
Domain of f = all positive integers =Z+
Range of f ={1,2,3,4,5,6,7,8,9} assuming 0 is not in positive integers
