Find the domain and range of these functions. a) the function that assigns to each pair of positive integers the first integer of the pair b) the function that assigns to each positive integer its largest decimal digit c) the function that assigns to a bit string the number of ones minus the number of zeros in the string d) the function that assigns to each positive integer the largest integer not exceeding the square root of the integer e) the function that assigns to a bit string the longest string of ones in the string

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Find the domain and range of these functions. a) the function that assigns to each pair of positive integers the first integer of the pair b) the function that assigns to each positive integer its largest decimal digit c) the function that assigns to a bit string the number of ones minus the number of zeros in the string d) the function that assigns to each positive integer the largest integer not exceeding the square root of the integer e) the function that assigns to a bit string the longest string of ones in the string

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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 assigning each pair of positive integers a domain shall have the first integer of the pair equal to each pair of natural numbers ie, N x N where N = {1,2,3,} from the set of natural numbers all integers are positive.

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 a domain of all such positive integers that we will have

Domain = {1,2,3,}

The 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) The domain is a piece of string ie

Domain = {0, 1, 00, 01, 10, 11, …}

The range includes the differences 1 and 0 in the string. Hence, we can have all positive and non-positive values ​​(0 and negative integer) 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 a domain equal to a set of positive integers ie,

Domain = {1,2,3,4,}

The range is the largest integer that does not exceed the square root of the number. Therefore, image 1 will be 0, image 2 will be 1. So the range will be a set of integers.

Range = {0, 1, 2, 3, 4,}

e) Domain = {0, 1, 01, 10, 11,} (String bit)

The longest wire in the string will give the range

Range = {1, 11, 111, 1111, 11111,}