Composition of Functions

[jituyadav1000]

you are the best MATHS teacher in youtube , after KHAN

[MathLogicals]

I really want that you will be my tutor , but the problem is im not in US . Im in UK .

[DudeUForgotAmmo]

Your voice is as soothing as Bob Ross.

[lionalfaizee]

Thanks you are saving me from getting mentally ill..

[EpicBeingxD]

Can you be my teacher! D: ...you are amaazing at teaching ^-^ Thanks alot im doing good in class cus of u :D

[motorstormers]

thanks a lot patrick :) nice hand writing :D

[qiuwygum]

Thanks for saving my liffffffeeeeeeeeeeee! You're a great teacher!

[videowatcher9596]

thank you soooooo much

[androcci]

how about the restrctions of the domain?? do you have a videos on that?

[DUBReviews]

thumbs up if your watching before a test

[metaldave08096]

Pat, i'm gonna share your videos with my class mates, if that is ok with you????

[joshcereal85]

DUDE. You saved me from staring at my hw for daaays -_o , THANKS :D

[RoxyRoller42]

Thank you so much for the help! You seem to have a natural knack for math! You pretty much taught me factoring last semester and so far composition of functions this semester!! Yay!

[patrickJMT]

@RoxyRoller42 glad i could help :) come back any time

[MathLogicals]

@patrickJMT , i wish you were my kumon teacher . My teacher taught me for about 10 minutes and learned nothing . My mom said that i shoulg go to my teacher and let him teach me how to solve this and what is this . I replied back to my mom and said Internet is a better teacher than my kumon teacher . I really hate kids that says our teacher sucks and most of my classmates dont like math so as a result , i got to teach them this .

[sheistyindividual]

i need help with f(3x-5) where f(x) = 1/x -x

[Shizune]

it all makes sense now when doing these thank you so much!

[Escov93]

Thank you so much your videos are a grade saver

[ilovegir44]

I really wish I saw this video last week, I just got my test back and failed horribly...LOL

[patrickJMT]

@ilovegir44 ah well, you will know where to go next time now : )

[NoRestRS]

I know you probably get a ton of these, but I have a quick question:

For composite functions, would g^-1 o(h o f)(x)

mean the inverse of g o (h o f)(x)? If not could you explain possibly?

Thanks

[TheBscit]

Patrick your tutorials are very helpful. But can you explain how im supposed to find the one of the functions if im given the compsite and another function? Say i was given F(x) and f(g(x)). How would i find g(x)?

[patrickJMT]

@TheBscit i have videos on this somewhere i think

[BenOmarbaOmar]

Patrick don't get me wrong! What I mean is fog and gof same as fof and gog? Thank you :)

[patrickJMT]

@BenOmarbaOmar not sure what you mean...

[BenOmarbaOmar]

You didn't do fof and gog!

[patrickJMT]

@BenOmarbaOmar was i supposed to?

[BenOmarbaOmar]

When you get the answer how to define them as domain and range?

[thecrticman]

you explain very well. none of my math teachers can compete however could you speak a little louder so that my mom doesn't freak when she sees the volume setting

[qwerty96232]

tqvm!

[Fallingstarswish3]

Excellent really useful

[flutilicious2]

Can you please post another video with a couple other examples for more practice! Thanks!

[statueofluberty]

its like function-ception XD function within a function!

[droduner]

Thank you so much. I am dying in this class after 10+ years away from higher math. This was a great explanation.

[missleslielicious]

thank you so much I effin' love u wish my teacher would explain the content like you!(;

[Raghad1M]

Be my tutor </3

[Adrian22Frets]

Why does my textbook make it so darn complicated!? Thanks Patrick..by the way, does the composition of applications work the same way?

[XTorMSnipers]

omgggg man your the best i love you

[cutecurlytop409]

aghhh i'm so glad i found you, your videos are incredibly helpful :)

[madhu2246]

your explaination is far more better than my lecturer thank you so much :)

[kevinopolis26]

My teacher never taught us this but he gave us homework, so long story short you saved me.

[staral8642]

thank you ssssoooo much i thought i couldn't do my project but you just helped and i feel sooo much better. thank uuuuuuuuuuuu

[CaliBoiHugo]

I have math final tomorrow and I think I'm gonna pass because of you.

[Jonl356]

Why can't math teachers ever explain it this well?

[AznHoboOVER9000]

I'm Asian and I learn from you.

YOU ARE A GENIUS AMONG GENIUSES.

[xtinacucu]

THANK YOU SO MUCH!

[TJFITZ41]

Thanks I have a quiz tomorrow this really helped me

[harshalchaudharyk]

best thing about your videos, you stay connected with all your viewers and reply to a bunch of comments. Respect brother ps. (the math part is the best)

[kingkrazy0wns]

test tomorrow, wish me luck!

[allanpeter7700]

left handers are awesome

[MrGersonnnnnnn]

ur my hero just helped me pass my exam

[00bbygirl]

wow i have been struggling in my algebra 2 class but after i saw this video man i have been doing really good now thank you a lot

[SimpleeAndrea]

so in my class we just began to learn about compositions. my teacher did not bother to teach us how to deal with rational exponents in class. so i was wondering if you could make a video on how to deal with this material. (p.s the problem I'm stuck on asks you for the f(g(x)) when f(x)=4x^-5 and g(x)= x^3/4)Oh and I desperately need to learn this because the chapter test is next week!>.<

Thanks!

[chuckcbaker]

great video!!!!

[thiebvan1]

Your voice is beautifullll.

[patrickJMT]

@thiebvan1 hahaha, thanks!

[gravyhouse]

if you haven't already, you should totally get a job as a math tutor. students would love you

[patrickJMT]

@gravyhouse i still do a bit of private tutoring, and people do love me : ) and i love them too! when you teach, no one wants to see you. when you tutor, you magically become the hero!

[gravyhouse]

@patrickJMT I think it's because many math teachers aren't able to give much attention to sepearte students who may be struggling. Tutors are awesome because they're there to help you learn and go at your pace of understanding. It's much harder to do that in a math class with 10-20 ppl in it.

So I speak for all the people you've helped when I say THANK YOU SO MUCH

[tasgraff420]

FUCK MATHS J,M,T Better stand fot JEDI MIND TRICKS!!!

[elizey7]

so what would you do if f of x is a single term?

[Twinsfan36]

Thank you so much!

[MTAL4ever]

is it possible for F o G and G o F to be the same?

[patrickJMT]

@MTAL4ever yep, but they do not have to be. if they are equal, the functions are inverses of each other

[cristylou7]

Your videos have been carrying me through my college algebra class. Thank you so much!

[hallowtrip]

10 people still failed the test

[gokharol]

I think Ive been through this in class this year... Yeah...

[mrmaaza123]

Hey could you please add some videos for equivalence classes ?

[iLhabxasianvids]

thanks for the help!!!, today is my Exam and i need to understand it....!!!! GOOD JOB :D, it mean a lot to me :DDDDD

[xmostwanted7x]

You make life so much easier, I can't thank you enough.

I was struggling with math, Trig/Alg2, and watching your videos when I would come home helped me 10x more than reading books/textbooks/guidebooks.

Thank you.

[suenge]

g(x+f(x))

what does it mean

[patrickJMT]

@suenge it means replace all x's in g(x) with ( x + f(x)) , whatever f(x) is

[Mantilak]

Hey man how do i do that oif it was f(x^2-1)=2^2+4 g(x)=3x+2, find (f o g)(2x-1)

because my teacher got a number in in the f(x^2-1)=2^2+4 to cancel out that squared i think it was a +2 and he got 2x+6 but i didn't get where he got that number from can you make a video about that

[Itsmyfaceonthescreen]

i take online school and sometimes its really hard to understand whats going on when you only have it written in front of you, your videos are a HUGE help and i appreciate it :)

[patrickJMT]

@Itsmyfaceonthescreen happy that i could help you : )

[Sarrahthenarrator]

Honestly, your youtube videos are the biggest help. Your videos are the PERFECT study guide. Thank you so much and keep up the amazing work! :)

[patrickJMT]

@Sarrahthenarrator glad you like my videos : )

[fglez17]

can you please teach at my school! your awesome!!!

[0ctaviaJade]

Thanks man. I appreciate it

[fuckpennyfinderz]

really good just the left hand writing is a bit complicated for me to read because it blocks the view and my focus on the problem itslef

[Darkknight5x5]

Thank you so much patrick! I understand it now:D I appreciate a lot for helping people out:) I was clueless on how to do this but you somehow did the impossible :P Thank you

[nanokd]

ur videos are actually really helpful most of the time but this 1 just confused me even more.....:(

[Lalasays15]

Are you a math teacher?

[jesikuhzeelayuh]

I WATCHED THIS, THEN USED THE POLYNOMIALS I HAD AND GOT A RIGHT ANSWER BY MYSELF!! OR THE FIRST TIME OF MY LIFE I LOVE YOU!!

[spinynorman1982]

@jesikuhzeelayuh I'm jut getting into math myself and I know your joy of a right answer!

[patrickJMT]

@WeAreToxicGaming come visit any time you get confused. hopefully i can help : )

[fnjdr4la]

Like my math teacher says:

"Just because it is long does not mean it is hard!"

[patrickJMT]

@fnjdr4la awwwwww baby!

[sweetfireslice]

help me with composition of functions with fractions!

[synamint]

Thank you so much!!! I totally get composition of functions now!!! You did an amazing job of explaining them!

[GreekMath1]

you deserve a youtube partnership

[transilvanianson]

@GreekMath1 I agree!

[Lateilla]

wat do i do if i am given the result of f(g(h(x))) and told to find the 3 functions that gave this result? i have no idea how to even start to do this in reverse!

[ninjapie117]

Missed two of my Math 120 class and this helped very mucho! Thank you sir!

[000darkprincess]

Thank you so much! You at better than my teacher. He totally sucks and never wants to help me :(

[rainbowpantiez]

if it wasnt for you i would be failing pre-cal!

[luffoutloud]

how do you find the domain of composite functions?

[11matt1]

thanks alot man you really helped!!

[IanGPx1]

what if f(x)=3 and g(x)=5, what do you do then?

[stiffsrs21]

LOVE THIS GUY!! LOL

[ismekin]

Hi Patrick, can you please make a video of this subject but working backwards? For example, given a complicated function f(g(x))= something, find f and g without using the identity function. Thanks!!

[Judaybutay]

i love you

[IBleedBlue2211]

You are my study guide and work perfectly!

[patrickJMT]

@IBleedBlue2211 wonderful! i am always here ; )

[PeanutJaz]

@patrickJMT Perfectly explained, thank you.

[ofkokf]

@patrickJMT hey, i was wondering if you still have your notes and examples (like the ones used in this video) because if i could download a .pdf file of them to print out it would help me in math class. Thanks.

[patrickJMT]

@ofkokf nope, i do not keep them

[hobo9596]

wow. i had this right all along, my teacher switched around the order and did it wrong. Confused the crap out of me

[TheProphetJebus1995]

Clear handwriting + Clear voice = Good Maths tutorial

[ClockwiseRobin]

Also, I was wondering of you can do one with fractions? I am in need of help with that.

[ClockwiseRobin]

Thank you so much! My professor is German so I can't understand him for the life of me. You're awesome! (:

[rarasatilb27]

you should be a teacher! I got a good score for my math test, thank you so much! :)

[granolup]

i'm jealous of your neat printing

[Lalitamm]

omg thank you so much! you make it way easier for me to understand then my high school teacher explain it!. I am so glad I finally understand it :D yay happy lol. You gotta be my personal youtube teacher. XD

[Jeezy21117]

Thank you!

[scorpnay13]

Dude!!! Thanks for saving my butt on this one : )

[Starinho509]

You're the best! 

[SodaJoker]

I'm trying to do a (fog)(x) problem with f(x)= 4x^-5 and g(x)=x^(3/4)

I can't figure out to do it with the negative and rational exponents.

[messirocker1010]

@SodaJoker Have you figured out how to do it if you have id appreciate if you could explain how to do it.... I have an important test coming up.

[SodaJoker]

I love you. nuff said

[thekidsnextdoor2]

Thank you so much! I totally forgot this after my lesson today, but you definitely refreshed it in my mind. I will be sure to subscribe and refer to your lessons when I am stuck. Thank you once again~

[hannahnymous]

very helpful! Thank you!!

[IamAeroDynamic]

thanks!!!!

[dhitalrajan60]

what happen when f(x+2)=x+4



[teenyweenypolkadot]

your explanations were straight to the point, easy to follow & so very helpful! thank you :)

[chibiladychoi]

 Why do I easily understand math problems on youtube? Why can't I understand our lessons in math inside the classroom? Dude, keep up the good work. Nice job. :)

[ahrkeytek]

@chibiladychoi because you cant pause and rewind in the classroom =P... or because your teacher sucks lol

[AnnFoster101]

@chibiladychoi I ask this question all the time



[bennydraws]

equation within an equation... INCEPTION!

[jomz149]

so whats this? (f+g)

[Warriorjemgi]

what about proving a composite functions exists? My lecturer said something about the domain of f(x) has to be a subset of g(x), but I can't remember exactly what he said AND I missed notes at that point.

Help?

[jomz149]

@Warriorjemgi yeah me too



[JLchevz]

Very good video :D

[TheAiraPatricia]

at 3:37 is there some kind of formula to follow to combine light terms?

[tlucasdeanegiles]

very helpfull brada! cheers bro

[JellynCrackers]

Ha ha ha....(5:27) "everywhere there's an x I have to plug in all of this mess". Love that you can relate to the students. You've been most helpfull!! Only wish you were right handed...but no biggie! You're super cool for clearing things up for me. Thanx a billion!!

[gilmoregirl0306]

you totally saved my butt. i'm doing an independent study course for precalc so i have no teacher and the textbook is absolutely terrible. you are a godsend!

[IcedKirby]

I found this video difficult to masturbate to.

[wysteriaglitz28]

i really admire people that are r good a math and ure one them but the only difference is that ure sharing what uve learn in a understandable way:)ure simply genuis!!u really help me a lot:)coz i have a poor performance when it come math..,so tnx!more power and keep sharing..thumbs up if u like him like i do!

[2439798]

Wow what an awesome video....I would say that this is on the level of Khan Academy, Thanks a lot Patrick!!!!!

[xXmoonshadow07Xx]

@6:39 how do i know if i'm required to square including the negative sign

[neogeo328]

Hi, Patrick. Your videos are great! A semester has passed since I did curve sketching, and your video has helped me remember pretty much everything we learned!

I was wondering, could you please make a video on how people come up with functions to describe certain things? It sounds vague, but I'm curious how people find equations and such for, say, something they want to build that has a very weird shape. You'd need a function to integrate, wouldn't you? So how do you get that function? Thanks.

[Winkxgirl25]

You'll be the reason why the world has more scientist and doctors. You're really making a difference. I'm a huge fan! Thanks. :)

[Winkxgirl25]

Good work, as always. :)

[157tty]

i from Brasil, thankys !

[m417k]

solve this for me g(f(10))

[PulseIndustries]

Way better than my teacher described it. I might be able to turn my failing math grade around because of you! I've been stuck on this all weekend but I think I have it now.

[HazelnutFrappe]

Thank you so much!!! you don't know how much help you were for me!! I previously had needed some help on rephrasing on some of these things and you have made it so CLEAR to me, now this thing is way to easy of a concept for me!! However, like all things they need practice but I know I can always get review from you if I may need it, Thanks again :)

[mrsobi2010]

great explanation! thanks



[mrsobi2010]

you are so good in simplifying things. thank you

[fishNguitars]

how the hell are you supposed to do this when you have an arrow diagram?!!

[AngieStarr85]

This is Extremely helpful. Do you have a video for decomposition of a function?

[davidrajecki]

This helped me soooooo much thank you.

[HoldTheMayo904]

I commend you for helping people out!!! Not many people in the world thats willing to use their time to help other. Hats off to you!!!

[iheartkittys71294]

what do i do if i m trying to find the domain after the composition

[trinidad128]

I appreciate the great video. I have a test tomorrow, and these were simple, but excellent examples for me to base my problem solving on. thanks!

[rachel1590]

@XxlilGelixX can u explain why ??

[wespim09]

I need help with this exercise. I have a test next Monday and I am confused.

find f+g, f-g, f*g, f/g and find the domain.

f(x) = square root of negative -x and g(x) = 4/x+4

[megaaf10]

dude! thanks a lot for sharing this video!

[XxlilGelixX]

uuhm why is it that in that question when we're trying to find g(f(x)) it was like this:

g(x^2+x)

4-(x^2+x) ?  I thought it supposed to be 4-x(x^2+x) then foil to get the answer... :/

-x-x+4?

[rachel1590]

@XxlilGelixX EXACTLY !! i wanted to ask the same .....

[XxlilGelixX]

@rachel1590 yeah I was confused then I understand why it's like that now. :D

[23idkyou]

please come be a teacher at my school. im in 10th grade in accelerated math 2 and my teacher does not explain anything like you do.

[rachel1590]

Its difficult for me to understand math which makes me frustrated wen i cant get through it,i have completed all the subjects of diploma except math,i cant escape it and i have no way around it,so i have to face it,my lecturer is not so approachable hence i cant turn to her for help,a personal tutor is so expensive which i cant afford hence you are my last hope,my exams are in may and you are making my life so much easier,LOVE YOU n THANK YOU SO MUCH from the bottom of my heart,GOD BLESS you !!

[XxlilGelixX]

@rachel1590 Big UPs to this guy!

[immissvintage]

Thank you so much..!!!!!!! Appreciate it, i mean it! THanks Thanks

[thehousefox]

I've decided I'm going to rely on your videos to teach me calculus! Hah, that is. I have to take it next year. But I plan on using all your videos ;)

[Ash0Can]

I love watching your math videos to review!

Thankss so much

[EdenBlade17]

Thanks for your videos man, as a ninth grader taking Algebra 2 my teacher goes a bit fast, so it's helpful getting some nice explanation outside of the classroom.

[rkohhhy2j]

i know HOW to do it, i just cant grasp which one is which, ie, f(g(x)) vs g(f(x)), ill do the work right but not know which was actually which