Composition of Functions (Precalculus - College Algebra 48)

A re-introduction to composition of functions and how to perform them.

[davidx]

Professor needs to get an award for these videos.

[stillattherestaurant]

You teach me more in 10 minutes than my trig teacher does in an hour and a half

[raulmd]

Professor, you have such a talent to simplify math topics. You are a God send, thank you for your videos!

[spritenoicy]

Big shoutout to you, sir! I am absolutely cramming right now but now I'm cramming with dignity

[madebyyuzz]

thanks in advance, your videos always help, I don't even need to watch it to be sure of myself.

[camillaliu]

You are so awesome. I am a newbie math teacher from China. Your video gave me a lot inspiration during my preparation on my class. Thanks a lot again!

[ZmQuad]

I am reviewing this video because I am taking Calculus, got to the “Chain Rule” and just blanked out. I did not know what a composition function was. I went through 7 tutors and the final one had good insight, “There is a difference between an Algebra problem, and a Calculus problem” with respect to why you are not understanding something. Turns out, my problem wasn’t Calculus, it was Algebra. funny, in that I had the exact same problem with “f(x) and f(x+h)”. Who helped me solve that? Super Leonard. I come back for a similar problem … same solution. I know you probably joke about “Blank Spaces” but I cannot properly explain how critical this explanation has been in my understanding of mathematics. Thank you very much good sir, and I hope that you have a good one.

[bekahsnell]

Thank you for breaking this down and going slow . Finally I get it !!

[georgesadler]

Professor Leonard, thank you for a solid computation and analysis of the Composition of Functions. These problems are really fun to solve in Precalculus/ College Algebra.

[shaed]

You are the best math teacher I have ever watched over youtube . Thanks lot

[Arafat-myfe]

It is definitely not as inspiring to teach when a number of students in front of you staring at you with amazement and bewilderment as to teach when you see literally none before you, let alone comes up the matter of amazement. Notwithstanding, Professor is doing all these for us and partly to sate his own satisfaction, indeed, purely out of his passion and utmost love for math.

[ryanbeatbox]

It seems like a good way to remember how you place the function in a composition is for example:

(f o g)(x) = f OPENS FOR g... the o obviously means "of", but for me remembering the placement could also mean "opens for". So the variable in (x) in f(x) opens for g(x) ... Same logic applies to every other thing too. I know after you do these a lot that won't even matter since you'll build up the memorization for where to put what, but this seemed to stick with me once you mentioned the variable opening up.

[imanhaji]

Great professor, great personality your contribuition to world is to much, thanks alot(winds from Somali coast)

[rayj]

Dear professor please do a series on linear algebra. Thanks again for all that you do#GOATprofessor

[mohammadjalal]

Professor, I can't thank you enough, your videos are the best

[Algebrainiac]

This was my favorite topic in Precal. Super fun. Amazing lecture 💖💖

[cartierdavid]

oh my god 🙂‍↔️🙂‍↔️🙂‍↔️ my teacher made this seem more complicated than it needed to be, thank you!!

[joecool]

FINALLY, a youtube professor that explains COMPLEX problems. Thank you. (are you Clark Kent?)

[blackphantom]

Thank you
You made this lesson so simple and explained everything well now I’m ready to take my final

[caroline]

thank you so much for such a great explanation! truly a life saver