Question

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

Answer 1

To get G^-1 all we need to do is flip the points around Example for (5,3) make it (3,5)
Here are the points in inverse (3,5); (3,2); (4,6)
To tell if a group of point can be a function we need to 1st look at the x values.  If all the x values are different, then it is a function (the x's are not all different)
If there are x values that are the same, they MUST have the same y value.
look at the points (3,5) and (3,2) those have the same x but they go to different y values so it is not a function.

You can think about it like this.  Can you go to more than 1 place at the EXACT same time?  Obvious answer is no. Can you have multiple people go to the same room?  Sure that is possible.  Same with functions.  An x value can ONLY go to 1 y value, and many different x values can go to the same y value.