The domain of your function consists of a point in a plane. While the function being 1-1, the point in the domain has exactly one image in the real number line. In other words, the range of the function is not equal to the codomain, which should tell you something.

Here, I want to define my own function say

. The domain consists of only one point. I would check to see whether the image is unique. See if it's

. This implies that

, which means that

and

. This also implies that the function is 1-1. This should not be hard since it involves only plugging something into a machine,

just like putting money into a vending machine and get what you wanted. If you put money into a vending machine wishing to get an item and end up getting two, then you know the machine is out of order.

For unto function, the range of the function must equal to the codomain. Now, suppose that I am the owner of the vending machine. I have all my items displayed, say 50 cans of soda, and expect a dollar for each can, but I have only customer who has only a dollar. All I could do is sell a can of soda. I have no takers for the remaining 49 cans of soda. That's bad new, which I would say, my business is

**not onto** my expectation.

Of course, no one would pay a dollar for a can of soda. Extortion, eh?