Which function has an inverse that is also a function?
{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}
{(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)}
{(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)}
{(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

Question

Which function has an inverse that is also a function?
{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}
{(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)}
{(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)}
{(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

myininaya · Answer

For each set reverse the numbers in the ordered pairs. 

Like for example 
Let's say F={(x,y)}
Then you would the inverse of F={(y,x)}

myininaya · Answer

Do just the first one for now?

anonymous · Answer

I thought it was A because the numbers are switched around. (-4,3)(4, -3)

myininaya · Answer

Why do you think it is A?
I'm not saying you are wrong or right yet.

anonymous · Answer

{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}
{(3,-4), (7,-2), (0,-1), (-3,4),(-7,11)}

anonymous · Answer

Sorry, not sre why those question marks are there

myininaya · Answer

The following is a function {(3,5),(5,3),(-4,3),(4,-3)}
But this one {(3,6),(3,7),(4,9),(5,9)} is not a function because there are two ordered-pairs with the same x-coordinate but different y-coordinate (I'm talking about (3,6) and (3,7)
These right here are not from your problem. I was just making up an example of a non-function and a function.

myininaya · Answer

I will take a set from your question
This is choice D
{(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}
Choice D is a function 
But is the inverse of a D a function?
 Well the inverse of D={(4,-4),(-1,-2),(0,-1),(1,4),(1,11)}
This one is clearly not a function because you have (1,4) and (1,11)
These points have the same x but different y.

For it to be a function, you cannot have more than one output per input.
For example you cannot have $$D^{-1}(1)=4 \text{ and } 11 $$
This would make inverse of D not a function.

myininaya · Answer

So my question to you is why do you think the inverse of A is a function?
(Remember I'm not saying you are wrong or right)

anonymous · Answer

I think A is a function because there are no repeated x functions

myininaya · Answer

You mean when we reverse the numbers in the ordered pairs
(when y becomes the new x)?

myininaya · Answer

You are right when we reverse all the numbers in the ordered pairs all of the x's are different so we are safe to assume the inverse of A is a function.

myininaya · Answer

Good job.

anonymous · Answer

Thank you so much for taking the time to explain why!

myininaya · Answer

No problem. 
:)