1a) Let A = {1, 6, 12}, B = {0, 2, 12}. The following are all relations from A to B, but which are functions? Explain why or why not? f1 = {(1, 2),(6, 0),(12, 12)} f2 = {(1, 0),(1, 2),(6, 12),(12, 0)} f3 = {(1, 12),(6, 0)} f4 = {(1, 0),(6, 0),(12, 2)}   (1b) Let X = {a, b, c, x, y, z} and Y = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Define a function f : X → Y to be: f = {(a, 2),(b, 3),(c, 7),(x, 9),(y, 4),(z, 8)}. Define a function g : Y → X to be: g = {(1, b),(2, c),(3, b),(4, a),(5, z),(6, z),(7, b),(8, x),(9, y)}. Determine the following: 1. The range of f. 2. The range of g. Do we have Rng(f) a proper subset of Codom(f)? What about for g?

Q: 1. Which of the following relations is a function? {(0, 0), (0, 1), (0, 2)} {(0, 0), (1, 1), (2, 4)}…

A: A relation R : X→Y to be a function, every element  x∈X should be related to a unique y∈Y. That…

Q: Which of the following relations is not a function? O [(1,2),(3,4),(5,6),(7,8)] O…

A:

Q: f={(-4,-7), (1,-4), (8,1)} and g={(-7,9), (1,8), (3,7)} find g of f

A: Given query is to find the composite function g of f

Q: Given that A = {1, 2, 3, 4, 5} and B = {x, y, z}, determine which of the sets of ordered pairs…

A: 1.  i) This ordered pair doesn't represents a function because the values 'y' corresponding to x= 4…

Q: 2. For the relation {(-3,15), (-1, 5), (0, -5), (1, 15), (3, -1)}, (a) Is the relation a function?…

A: Given relation:- -3,15,-1,5,0,-5,1,15,3,-1

Q: what is the domain of the relation (2,-1), (4,-2), (0,0), (3,7), (4,6)

A: The relation is given by the set of ordered pairs x,y, such that, R=2,-1, 4,-2, 0,0,3,7,4,6 The…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.