In this video we’re going to talk about composition of functions And just the notation, they’ll write F, circle, G of X This is not a multiplication symbol. That’s why they try it like a little dot. You know denotes. That’s why they try to make it a little bit bigger Likewise, it’s not the word fog I’ve heard people ask me about fog x and I was never quite sure what they were talking about so It’s read F of G of x, and what this notation means is you’re basically plugging g of x inside of f of x likewise g of f of x means take f of x and plug it inside of G So I think composition is something that [confuses] people a little bit, so let’s take a couple examples so f of x let’s make that x squared plus x and Try to color code things here to make them a little bit easier to follow suppose we have g of x is let’s make [it] 4 minus x all right and A Couple things here suppose. We want to figure out f of g of x [so] again what that means is we want f of g of x and Well, I can plug in g of x I know what g of x is all right g of x is the equation [4] minus x So that’s what I’m going to substitute in there okay, so there’s [f] of g of x and you know kind of off to the side if somebody said figure out f of 3 what would you do well you would look back at your original f of x equation and everywhere there was an x you would replace it with a 3 So I’m going to do the same thing when I do this problem I’m going to go back and everywhere. There’s an x I have to put something in But this time the thing that I’m substituting in is not just [a] simple number like 3 it says I have to substitute in the quantity quantity excuse me 4 minus x so this is the idea with a composition of functions Instead of just kind of substituting a simple number in you’re putting in a more complicated expression So let’s simplify this one down. This is 4 minus x times 4 minus x plus just 4 minus x if I foil this out. I’ll get 4 times 4 which is 16 I’ll get 4 times negative x which is negative 4x negative x times 4 that’s negative 4x Negative x times negative x that’s positive x squared I have my plus 4 I’m running out of room here and my minus x still hanging out and now it’s just a matter of combining like terms, and I usually think take things in descending power, so I see an x squared I’ll write him first a Negative 4x and a negative 4x that’s negative 8x Minus another x that’s negative 9x so that takes care [of] my x terms And then I’ve got 16 plus 4 which is 20 and that would be the composition f of g of x Okay, let’s maybe take a variation on this one and let’s flip it around So again, I had that f of x is x squared Plus x and I had g of x is 4 minus x suppose now I want to find g of f of x and recall multiplication the order in which you do things doesn’t matter 2 times 3 is the same as 3 times 2 and This notation again. It almost looks like Multiplication, but it’s not so you have to be careful because in general you don’t get the same thing So notice I found f of g [of] x to be this stuff Now let’s see what we get when we do g of f of x so [again] this notation it says you plug f of x into [your] G function well again f of x is The [function] x squared plus 4 excuse me x squared plus x so it says I’m going to plug in x squared Plus x and Just like before if it said find g of 2 I would [find] my G function everywhere there was an x I would plug in a 2 Well now it says everywhere. There’s an x I Have to plug in all of this mess x squared plus x and this is now going to be the composition function g of f of x so if I distribute I’ll get negative x squared [I’ll] get a minus x term and then I still have my positive 4 hanging out and that’ll be the composition, so Notice I got something much different This is what I got when I did f of g of x and this is what I got when I did g of f of x so two totally different things there so just something to be aware of Suppose the original problem was to find g of f of [four] Let’s make it three just so I have a different number floating around the first thing I would do just like before [I] would just find g of f of x just like it is and I would get this stuff And now it says all you’re doing is you’re [just] replacing the x’s with [3S] So the [x’s] with threes, so that’s what I would do here and we get 3 squared minus 3 Plus 4 well, you square the 3 first so I’ll get 9 but then it will become negative 9 I’ve got a minus 3 hanging out a positive 4 well negative 9 [minus] 3 that’s negative 12 plus 4 that’ll turn out to be negative 8 whoops is all cut off negative 8 and that’ll be my solution So this is the basic idea with composition of functions You’re basically just putting one function inside of the other one So I hope these couple examples make some sense I definitely encourage [you] to try to rework them if they’re don’t if they don’t make a lot of sense Certainly feel free to send me an email. You can visit my website Just math tutoring [comm] there’s lots of other [examples] on there if you need to see some more Composition of function examples send me an email let me know what your problems are and I’ll try to get to them as soon as I can and I can post another video with a few more a few [more] examples on there, so Good luck with this stuff I think composition is probably of all the kind of operations with functions it can be the most confusing so Just try a few examples, and I think you’ll get there

OMG, I was so stuck until I found your video. It made it easier because of the color coordination I think whatever the case was, I completed all of my questions and got them correct in a manner of minutes versus days prior to finding your video. THANK YOU. Keep up the great work

Fog x lol

Thank you so much

If I would become a billionaire someday. I would donate you half of my net worth just because you teach what "formal teachers" fail to teach effectively.

really nice. Thank you.

you are sooo great . aaap ne bahut hi aacha samjhaja

I wish you were my teacher 🙁

That moment you realize PatrickJMT is the Organic Chemistry Tutor 😳 “in this video…”

why cant i download??

I legit did not know anything about this, within the first 46 seconds I understood it.

Done

This helped so much

thanks for taking the time to make this its still helping people almost a decade later

THANK YOU SO MUCHH

If you can't understand Patrick you need God!🤗🤗

You sir are my hero

(fog)(fx) how abt this

who here is watching this in 2018?

Back when highest video quality was 240p….

I don't able to understand by my teacher but u teaches well NYC teaching.

Made composition of functions a very easy topic. Thanks a lot

Easy way to find inverse

wait, in the last example, you did the x^2 first then applied the negative, but isn't that wrong? isn't it (-x)^2, which would result to x^2?

والله كش ما فهمت شعجب

Thank you!

I never knew that a lefty like me can have such a relaxing handwriting

I don't understand crap from this. This video is good but i still don't understand any of this 🙁

finally! i understand it very well

Thanks for this video, a big help indeed😊

Sar one help me please

you are the best

Thanks

thank you so much.. Pre Calculus is really confusing

Thanks!

Uhm… I know there are other ways to solve this but for me, this way of solving is the hardest

It's because of you I'm ready for my exam❤

thank you for this video

Im really a slow learner how did you get the final answer?

Studying before exam. Now I know.. Better than my teacher.. Thank you!

I have an exam tomorrow. Thank you very much

how did we get 4?

Why most of right handed persons are so intelligenr??

I learned composition in just 8 minutes rather than my teacher teaching 1 and half an hour thank you for sharing this bro

do you have a video about composition function like how to get the answer(g○g)(x)=? or (f○f)(x)=?

So appropriate method of composite…

sorry..composition of function…

I was getting it until he brought in 4-x^2

whats up fellow strugglers

😍

3:10 I seriously still don't get this! I literally am so confused. Why can't I do (4 – x)^2 + x ???

You noob, you perfectly know what "fog(x)" is when ppl ask.. Great video!!!

Why put x=3 ??????

Wow!Thanks a lot…I happen to be a slow learner..your patience made me understand this …I re watched 3 times to perfect it..hoping to tackle my exam this Friday well..

That was so helpful,thank u so much!!

Thanku

Thank you i was so confused somewhere between the sum and finally you and youtube helped me go on hit 1M sooooon

Fog x!!!!!

thank you bt this are so simply i have triky peoblems.

when 1 function is given and the solution of the orther functions are given then you are ask to fine fog…..

I came here to understand more but instead I'm more confused😅

I know im late but if anyone is reading this isnt (4-x)^2=(4^2)-2×4×x+×^2=16-8x+x^2

16-8x+x^2+4-x=12-7x+x^2?!?!?!

Thank youuuu!!! my math teacher is amazing but this wasnt clicking with me at all. i finally understand it!

Please more examples. Im getting a 72 in my class and we are doing these now. My teacher missed a class and is cramming this in a hurry because he took that day off. One more test then the final. Im totally having difficulty. I cant get below a 70 in this class. Thank you! You are calming and understand that every little thing can help like using different colors and explaining ways people tend to get confused

Whose there who r watching this video in 2018???

thank you

Thanks, was able to complete my section on this on Aleks. could not have done it with out watching this video. Thanks again.

Thank you

Hey Patrick, I have a question. My math final is on Monday and she barely introduced this concept. On the first example of composition of a function, the final answer was x^2-9x+20. Would you factor it or leave it in that standard form?

Also doing this method seems very complicated. I have another question, if you (g o f) (x) where did the 3 come from? I've watched this video multiple times, I just dont quite understand.

finals are tomorrow this helped a bunch , thanks

which of the following compositions makes B'(8,9) the image of B(9, -8)?

Best and basic explanation

Taşşaklarına beton yetmez gurban.

x=x =x

no morer mr X

im X men

I got a math add before the video

Thank you so much, very helpful!

thank you very much sir

Güzel anladım eyvallah hocam

Brilliant bro

i dint even understand how to put one function in other

This is so interesting and helping……. Thank you!!! All the way from Zambia

Happy 10 year anniversary. You helped alot of people in math

The video was not clear 😒

You’re really a real nigga for this

Amazing. Very easy method to understand 😘

Thanks a lot.

Just get tot he exam question waffle

Tnq so mach….❤

Given: f(x) = 2x+100

What is (f o f o f o f) (1)

My professor yelled at me and told me she wants to murder me because she skipped a bunch of steps you showed and I didn’t get it. This is why I hate math, all the step skipping, and lack of coherent written instructions! Thank you!

How it become 3??? f(3)??

Where it become from??? So hard!

bobo nito

i hope u read dis thaks alot

General Mathematics xD SHSlife

11 years late. Still, Thanks

Thnx!🤘🤘

Loved the vid made it a lot easier to understand

Putangina hindi ko maintindihan

nice im the one who watch his video around 11 years