Question

G = {(5, 3), (2, 3), (6, 4)} Is G-1 a function and why?

Yes, each element in the domain has only one range value.
Yes, each element in the range has only one domain value.
No, each element in the domain does not have one range value.
No, we don’t know the original function and therefore can’t make the determination.

Answer 1

No, each element in the domain does not have one range value.

Answer 2

The inverse relation G^(-1) is not a function. Why not? Because the y value y = 3 is paired up with more than one x value (x = 5, x = 2). The inverse relation G^(-1) is the set shown below

{(3,5), (3,2), (4,6)}

All I've done is swap the (x,y) values for each ordered pair to form the inverse relation. As you can see, x = 3 leads to multiple y value outputs which is why this relation is not a function. So in short, the answer is choice C. To have the inverse relation be a function, each value in the original domain must map to exactly one value in the range only. However that doesn't happen as the domain values map to an overlapping y value (y = 3).