[Discrete Mathematics] Inverses Examples 2

We do two more examples with inverses and proving that functions are bijective.
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Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[@Mother_Mia]

Thanks for these videos! You do such a nice job of explaining.

[@SuperSayiyajin]

Thanks a lot...

[@cristianosantana4987]

Could you, please, give an example of equation wich gives different X and Y when f(x) = f(x) is applied (injective test)?

[@saamenerve1869]

f(x) = x^2 Let f(a) = f(b) a^2 = b^2 +- a = +- b + a = - b

[@muhammedismail8299]

For the first one, what if the value of m=0??

[@Mother_Mia]

Well we were testing Y values. This probably should be modified to be any line that is not completely flat (slope equals 0). That particular line is not invertible.

[@brod515]

1:29 why did you say we get a unique x back? we don't know that its unique.

[@Mother_Mia]

We do know that it's unique though. In the first step, we proved that this function is injective. That means every x maps to a unique y. It is one-to-one. That means if x equals 2, then the y value will never be more than one unique value. This works in the reverse as well. We cannot have the same x value for multiple y values. For example, we cannot have (2, 4) and (2,6). That would not be 1 to 1 and thus would not be injective. And since we just proved that it is surjective, that means every y maps to some x value. With it being one to one, I can guarantee you that will get a unique x. Good question though! **** Another thought, if we had multiple x values for the same y value, like (2, 4) (5, 4), then that also would not be injective since two x values map to the same y value. Injective implies a 1 to 1 relationship with every x and y coordinate available so for sure you will get a unique x back.

[@brod515]

@@Mother_Mia yeah sorry. I'm not really sure what I was saying