Composition of Functions (Precalculus - College Algebra 48)

[@davidx5828]

Professor needs to get an award for these videos.

[@cheyennestewart5930]

You explained this so well with the "blank space" I was struggling, thank you !!

[@akkaradechinnok5325]

😊😊😊😊😊😊😊😊😊😊

[@akkaradechinnok5325]

😊😊9😊😊😊😊😊

[@stillattherestaurant]

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

[@raul21md]

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

[@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.

[@ZmQuad]

And side note: after his initial explanations, I was able to finish the equation for g(f(x)), f(f(x)), g(g(x), as well as the evaluations. However, after like 8 hours today of feeling like I’m dumb as a rock because the tutors kept explaining in the EXACT same way, it is very soothing and relaxing to come up with the right answers, and know that my logic isn’t totally flawed.

[@spritenoicy1676]

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

[@rosepierce9382]

You got this!

[@camillaliu3735]

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!

[@madebyyuzz]

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

[@lifeaspuleng6235]

professor Leornard for the win

[@bekahsnell8882]

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

[@rosepierce9382]

Yeah, that's what I like most about his videos, how he is so patient with us.

[@shaed3759]

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

[@georgesadler7830]

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.

[@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.

[@bunny4173]

yeah thats great ...the open hole suggests that too

[@I-Jalal]

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

[@Arafat-my6fe]

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.

[@rosepierce9382]

How are you doing now? Completed the playlist? 2 years late, but hope you're doing well.

[@mrmalone28]

Easy peasy…thanks to professor Leonard!!

[@imanhaji7166]

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

[@cartierdavid9440]

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

[@Algebrainiac]

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

[@blackphantom9024]

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

[@rayj1232]

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

[@caroline6461]

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

[@ltac8194]

Professor Leonard, for time stamp 23:55, I got -192 and not -196, however 192+240-74 also =-26.

[@rosepierce9382]

Yes, it's a mistake.

[@joecool9402]

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

[@satioOeinas]

Another great video Professor

Great class! Thanks! 💯🤓

[@jecs3300]

pls make a video about laplace transform

[@hazemturani5611]

Hello professor, will you do a series about Discrete Math?

[@fridahndumba8355]

Good teaching skills

[@paislietran]

i literally love you forever

[@K-206]

thank you

[@cobyup10]

Lol thanks for clearing the "fog"

[@maylingcheng1641]

Thank TOU so much u Are so helpful i luv u and ur Taylor Swift references❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

[@FreshJsTV]

very clear video

[@Kaution2004]

If this is college algebra then why the hell am i getting this in high school!?

[@ryanbeatbox]

This feels very similar to recursive functions in programming.

[@_Anna_Nass_]

Thank you !

[@tpthpt5973]

Great video!

[@rosepierce9382]

Professor Leonard: DO YOU SEE IT? DO YOU SEE IT??! AH MAN, YOU HAVE TO SEE IT!! The camera learning Precalculus: 👁👄 👁

[@shaed3759]

Would you please do a video about rotation composite along with some examples

[@ladyblue701]

@Professor Leonard, how do we solve a composition (fog) for f(y) and g(x)?

[@FettuciniPanini]

bruh you've been uploading math topics for over 8 years.....does math have no end???

[@ClemoVernandez]

Nope :)

[@irvlazaro7302]

Before Math Enlightenment.. Chop Wood, Carry Water ...After Math Enlightenment...Chop Wood Carry Water.

[@rosepierce9382]

Lmao, this is the funniest comment ever! I get your frustration, but at least we get to see Prof. Leonard.

[@Peter_1986]

I am not a fan of the composition notation; I feel that it is much clearer when something is written f[g(x)], instead of that weird (f∘g)(x) thing.

[@oliverosjevyp.6363]

i have an exam tomorrow. lmao binging the precal and the calculus 1 for 1 night AHAHHAHAH cause my prof didnt teach us lmao HAHAAHHAH

[@dashaagafonova519]

Это так же не бесполезно.)

[@rosepierce9382]

February 27, 2023

[@aromesalihu3765]

i thought he was henry cavill

[@Ifeelalonee]

Professor r u single?

[@SzuesS]

He is married to a woman named Lynsee. She is super sexy too.

[@rosepierce9382]

Yes, he's single. He's single-handedly saving all of our asses.