Answer:
a) Domain = N x N, Range = N
b) Domain = N, Range = {1,2,3,....,9}
c) Domain = {0, 1, 00, 01, 10, 11,...}, Range = {.....,-4, -3, -2, -1, 0, 1, 2, 3,......}
d) Domain = {1,2,3,4,.....}, Range = {0, 1, 2, 3, 4,.....}
e) Domain = {0, 1, 01, 10, 11,....}, Range = {1, 11, 111, 1111, 11111,.....}
Step-by-step explanation:
a) The function that assigns to each pair of positive integers the first integer of the pair will have domain equal to all pairs of natural numbers i.e, N x N where N = {1,2,3,.....} since the set of natural numbers has all positive integers.
Domain = {(x,y) | x ∈ N and y ∈ N}
The range is any integer so it will be a set of natural numbers N = {1,2,3,....}
b) Here, we have domain of each positive integer so we will have
Domain = {1,2,3,....}
Range is the largest decimal digit of the positive number which can be any number from 1 to 9
So, Range = {1,2,3,4,....,9}
c) Domain is a bit string i.e.
Domain = {0, 1, 00, 01, 10, 11,...}
The range includes the differences of 1's and 0's in the string. According to this, we can have all positive and non-positive (0 and negative integers) values in the range. So, it will be a set of all integers
Range = {.....,-4, -3, -2, -1, 0, 1, 2, 3,......}
d) We again have domain equal to set of positive integers i.e,
Domain = {1,2,3,4,.....}
Range is the largest integer that does not exceed the square root of the number. According to this, image of 1 will be 0, image of 2 will be 1. So, range will be a set of whole numbers.
Range = {0, 1, 2, 3, 4,.....}
e) Domain = {0, 1, 01, 10, 11,....} (A bit string)
Longest string of ones in the string will give the range
Range = {1, 11, 111, 1111, 11111,.....}
≈ 11.18
≈ 24.17
≈ 19.21