Discrete Math - 2.3.3 Inverse Functions and Composition of Functions

Practice with inverse and composition of functions.

Video Chapters:
Introduction 0:00
Inverse Functions 0:06
Show a Function is Invertible and Find the Inverse 1:57
Composition of Functions 6:46
Composition Practice 8:12
Up Next 11:43

Textbook: Rosen, Discrete Mathematics and Its Applications, 7e

[ecru_]

I am actually super lucky rn
The same textbook we use is the one that's used for this course too :0
Thank you so much! My professor is hard to understand and the powerpoints he uses are so bare boned and don't have alot of good examples to follow to completely understand the concepts. because of these videos, I now understand two chapters of what we have gone over so far!

[daniyelzhumankulov]

thank you a lot professor!!!! You are actually making a lot of things so much easier so that we, students, could understand it better. this playlist is much better than reading long textbook chapters.

[jeremyedwards]

Your videos are perfect to help out with class. If you did an intro to real-analysis series, it'd be amazing!!

[cameronsantiago]

This class reminds me of Linear algebra, which reminds me of calc3! It’s repeating itself

[_wessi_ford_]

This has helped me so much! Thank you 😎

[unruly_ronin]

Thanks so much Madam. You teach this so awesome

[peacemedhanie]

I like your explanation but the example feels easy .I wish you can do harder example

[barxco]

dont know if this may help but: the reason you need the function to be bijective to be invertible, is because otherwise the "inverse" would not be a function:
* by definition all elements of a function must have an image, and only 1 image.
so:
*if the original it's not one-to-one when you try to find the inverse you'll have at least one element on the domain with more than one image.
*if the original is not *onto* then when you try to find the inverse, you'd have at least one element of the domain without a corresponding image.

[hope-bvnc]

First of all thank you professor, and then I have one question in 5:36 that how can the function be onto with out the range(R) and the co domain(Z) being equal ?

[kadirbeksharau]

why it needs to be onto in order to be invertible? We could say that it is invertible such that y contains only 1, 3, 4

[lankeastor]

If the definition of "freak" is someone who has to write their formulas in a particular order, then I'm something of a freak myself.

[jonahrivera]

How do your videos have fewer views than other ones?

[Mauri]

So when trying to determine whether a function is onto, all elements of the y domain must be mapped to. Would that mean that a function of f: Z -> Z, where f(x) = x^3 is not onto? But if i were to change the domain from Z to Real numbers, it would then be onto. Is this correct?

[jacksonmadison]

while a function such as x^2 has no inverse under the codomain of all integers
would it have the inverse sqrt(x) under the codomain of all positive integers?

[uq.y]

Thank you so much that's really amazing❤❤❤❤

[kirkeduardbrazil]

Kini bitaw yawa wla mani pulos kung manar bahu ta yawa ngano apil2 pani SA mga exam

[emmanouilpapadakis]

Don't mislead the students telling them that you proved the onto. You did not. Examples are not substitutes for a proof or justification

[energy-tunes]

Absolutely shocking how American students of my age are struggling to understand the bare bare minimum for each concept yet I'm stuck here drowning in theorems :D