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.
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.
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.
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.
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.
Professor needs to get an award for these videos.
You teach me more in 10 minutes than my trig teacher does in an hour and a half
Professor, you have such a talent to simplify math topics. You are a God send, thank you for your videos!
Big shoutout to you, sir! I am absolutely cramming right now but now I'm cramming with dignity
You got this!
You explained this so well with the "blank space" I was struggling, thank you !!
😊😊😊😊😊😊😊😊😊😊
😊😊9😊😊😊😊😊
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!
thanks in advance, your videos always help, I don't even need to watch it to be sure of myself.
professor Leornard for the win
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.
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.
You are the best math teacher I have ever watched over youtube . Thanks lot
Thank you for breaking this down and going slow . Finally I get it !!
Yeah, that's what I like most about his videos, how he is so patient with us.
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.
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.
yeah thats great ...the open hole suggests that too
Professor, I can't thank you enough, your videos are the best
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.
How are you doing now? Completed the playlist? 2 years late, but hope you're doing well.
Great professor ,great personality your contribuition to world is to much,thanks alot(winds from Somali coast)
Easy peasy…thanks to professor Leonard!!
Dear professor please do a series on linear algebra. Thanks again for all that you do#GOATprofessor
Thank you
You made this lesson so simple and explained everything well now I’m ready to take my final
oh my god 🙂↔️🙂↔️🙂↔️ my teacher made this seem more complicated than it needed to be, thank you!!
Professor Leonard, for time stamp 23:55, I got -192 and not -196, however 192+240-74 also =-26.
Yes, it's a mistake.
This was my favorite topic in Precal. Super fun. Amazing lecture 💖💖
thank you so much for such a great explanation! truly a life saver
FINALLY, a youtube professor that explains COMPLEX problems. Thank you. (are you Clark Kent?)
Another great video Professor
i literally love you forever
Great class! Thanks! 💯🤓
Good teaching skills
Hello professor, will you do a series about Discrete Math?
pls make a video about laplace transform
Great video!
Lol thanks for clearing the "fog"
very clear video
Professor Leonard: DO YOU SEE IT? DO YOU SEE IT??! AH MAN, YOU HAVE TO SEE IT!!
The camera learning Precalculus: 👁👄 👁
thank you
Thank you !
Would you please do a video about rotation composite along with some examples
Thank TOU so much u Are so helpful i luv u and ur Taylor Swift references❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
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.
@Professor Leonard, how do we solve a composition (fog) for f(y) and g(x)?
This feels very similar to recursive functions in programming.
If this is college algebra then why the hell am i getting this in high school!?
bruh you've been uploading math topics for over 8 years.....does math have no end???
Nope :)
Before Math Enlightenment.. Chop Wood, Carry Water ...After Math Enlightenment...Chop Wood Carry Water.
Lmao, this is the funniest comment ever! I get your frustration, but at least we get to see Prof. Leonard.
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
Это так же не бесполезно.)
February 27, 2023
i thought he was henry cavill
Professor r u single?
He is married to a woman named Lynsee. She is super sexy too.
Yes, he's single. He's single-handedly saving all of our asses.