I taught math for 45 years, now retired. Tutoring a student in Precalculus so needed to brush up on this topic. Your explanation is clear, precise, well-paced, easy to follow. Outstanding!!
You are an excellent teacher. People like you should share their precious knowledge on UA-cam as you do with your relevant and clear explanations. Thanks a lot and please do more!
You know, when people say our professors aren't teaching us properly, its because they're speaking a more advance language and comprehension lv that we are not at yet. But a video like this where you speak at a language where everyone can speak and comprehension lv is also for everyone to understand, we can understand the most difficult things. I realized that by watching and you have my subscription (y)
If you have the gift of simplifying what others complicate, you make the complicated simple vs. others that make the simple complicated! Do the math of the accumulative impact for both cases on individuals, you realize that there aren't many like you in this world!
Mother of god! I understand! You are literally the single person on this earth apparently that has clearly explained the process for these problems and I thank you!
Probably the best explanation of domains of composite functions I ever seen. You went straight to the ones that stump the students --rational functions. All the others always dwell on polynomials, which are a lot easier to solve. Thanks for tackling the difficult ones!
I think your style of teaching math is the best I've ever seen. Every time I leave class confused, I just check out how you've explained and then the light bulb goes on! Awesome lessons, just awesome. Thanks.
I HAVE BEEN SEARCHING ALL MY LIFE FOR THIS OMG. I HATE MATH AND IM SITTING HERE CRYING AND I HATE MATH AND I FIND THIS AND GET IT LIKE GET ME PARADE, I HATE MATH BUT I GET THIS! THANK YOU FOR BEING AN AMAZING TEACHER AND MAKING IT SO SIMPLE TO UNDERSTAND
Thank you very much for doing this! Whenever my professor does it he does some crazy stuff explaining stuff way over our head and I'm lost completely. You did it and I understood it fully!
It's amazing that I've been in school since August, hardly learned a thing in Pre Calculus, and spent one day soaking up all the information required for my midterm tomorrow. If you administered an online class I could do it in a few weeks.. You're incredible!
wow , you explain things so well, I wish my professors knew how to do this.. it's so frustrating going to all of my classes and being confused throughout the entire lecture. im a slow learner so i dont catch on like everyone else. you have a new subscriber! thanx
I haven't seen integral notation before, I was taught to write it as: {xER|x=/=-1/2,1/3,0}. Meaning x is an Element of the Real numbers and cannot equal -1/2, 1/3, or 0. Nice video :)
This is the only video I've seen of this guy, and I've already hit "Subscribe." YOUR VIDEOS ARE SUPERIOR. YOU SHOULD BE VERIFIED ON UA-cam FOR BEING SO AMAZING
This is amazing. It's quite easy to understand. My sister actually asks me for help about this stuff but I couldn't remember much about functions anymorr so I did some research and happen to find your youtube video. After watching your video I would gladly share the link to her because it's really informative and easy to understand. ❤😊✌
omg thank you so much! i'm in precalc this year and had geometry last year and i could not for the life of me remember how to do this! you were awesome at explaining it, thank you so much!!!
thank you so much i was really confused since the teacher explained it in class but i was very tired that class and she made us stand up to watch what shes doing on the whiteboard (so i was more focused on my legs hurting cuz we stand up pretty much the whole class its kinda annoying idk why we have desks at that point) so i tried to check canvas if she wrote ANY information about how to do this and she didn't so anyway thank you so much
I think the domain should be {x/x not equal to -1/2 u 1/3} 0 is not included. Because if you replace x with zero in the denominator the answer would be -6. This is only my opinion feel free to correct me if I am wrong :)
Question: I notice that the domain restrictions of f(x) can be found by simply looking at the g(f(x)) equation. Is this merely a coincidence, or will it always be the case?
I noticed this too, for instance: f(x) = 1 / (1 - x), g(x) = (x - 1) / (x + 1) g(f(x)) . . . = ((2 - x) / (x - 1))((x - 1) / x)) = (2 - x) / x, for x 1 since (x -1) / (x - 1) is 1 Domain is therefore x 0, 1. Here, I determined that the domain of the composition can't include 1 without looking at the "inside" function f (although it was more work.)
The reason for this is that sometimes when you simplify, you "miss" a number that would otherwise have been excluded. For example, say we have g(x)=1/x and f(x)=1/(x-4). If we compose and simplify g(f(x))=1/(1/(x-4))=x-4. Notice that this simplified version of g(f(x)) has no domain restrictions. However, before we simplified it, we still have the domain restriction x=/=4. Sometimes this matters, sometimes it doesn't. It depends on the context on the problem, but, it's always better to be safe than sorry!
When it comes to interval notation of the domain, wouldn't it be more clearer to write: R\{-1/2,0,1/3}? It means the same thing, just in a less tedious format as opposed to naming all the four intervals between those values. Just some constructive criticism, aside from that: good video!
+Natalie Elizabeth That would make it set notation. Not interval notation. So if the question asks for you to put in interval notation then you may not get the mark.
So the domain of f (x) woun't be included with the domain of (fog)(x) ? So the domain of (fog)(x) would be from negative inifinty to positive infinity exept the zeros of the input function -in the this case g (x)- and the zeros of (fog)(x), right? *So the domain of f (x) has nothing to do with all this, meaning I don't have to exclude it's zeros from the domain of (fog)(x), right?
how would you find the inverse of f(x,y)=(2y-x,x+y) for f: R^2 => R^2, I found your video very helpful but i still cant figure out how to do the question above, Could you help me?
If you look at the rule: "range of inside must be contained within domain of outside" this function is not defined, so it probably was not a very good example, as it could confuse some people. Just a friendly warning!
I'm a little unclear how X can be equal to two different values within the same argument. -1/2 and 1/3 at the same time. I can see it if you were talking about a curve on a graph where it crosses the X axis in two places.
would you download video have this example of composition : f(x) = 1+x / 1-x , g(x) = x / 1-x find fog(x) and gof(x) and find their domains if you solve it i will be so happy :) **i hope that you solve this equation as soon as possible**
Simple, if you simplify the equation before finding the domain, there is a possibility of a zero(or any number that would make the equation invalid) being included in the equation when it should be excluded because it makes the equation invalid.
This was made 7 years ago, but it's still so helpful in helping me study for my test tomorrow. Thank you!
9 years ago now 🤡
@@MarioplushJean oh wow
@@QueenVictoria26 this video is helping me study for a test lol
Im a Freshman in Pre calc
@@MarioplushJean I'm a freshman in college
I taught math for 45 years, now retired. Tutoring a student in Precalculus so needed to brush up on this topic. Your explanation is clear, precise, well-paced, easy to follow. Outstanding!!
You are an excellent teacher. People like you should share their precious knowledge on UA-cam as you do with your relevant and clear explanations. Thanks a lot and please do more!
You know, when people say our professors aren't teaching us properly, its because they're speaking a more advance language and comprehension lv that we are not at yet. But a video like this where you speak at a language where everyone can speak and comprehension lv is also for everyone to understand, we can understand the most difficult things. I realized that by watching and you have my subscription (y)
I relate to this completely!
If you have the gift of simplifying what others complicate, you make the complicated simple vs. others that make the simple complicated! Do the math of the accumulative impact for both cases on individuals, you realize that there aren't many like you in this world!
Mother of god! I understand! You are literally the single person on this earth apparently that has clearly explained the process for these problems and I thank you!
dude..seriously...u are the reason i didnt give up on engineering maths and you are the reason i passed my maths tests...thank you is not enough
Probably the best explanation of domains of composite functions I ever seen. You went straight to the ones that stump the students --rational functions. All the others always dwell on polynomials, which are a lot easier to solve. Thanks for tackling the difficult ones!
I think your style of teaching math is the best I've ever seen. Every time I leave class confused, I just check out how you've explained and then the light bulb goes on! Awesome lessons, just awesome. Thanks.
you are my favorite online math tutor, you have a certain way of explaining that a lot of people including myself can understand. thanks so much!!
I HAVE BEEN SEARCHING ALL MY LIFE FOR THIS OMG. I HATE MATH AND IM SITTING HERE CRYING AND I HATE MATH AND I FIND THIS AND GET IT LIKE GET ME PARADE, I HATE MATH BUT I GET THIS! THANK YOU FOR BEING AN AMAZING TEACHER AND MAKING IT SO SIMPLE TO UNDERSTAND
i wish i could understand this crap...
Thank you very much for doing this! Whenever my professor does it he does some crazy stuff explaining stuff way over our head and I'm lost completely.
You did it and I understood it fully!
It's amazing that I've been in school since August, hardly learned a thing in Pre Calculus, and spent one day soaking up all the information required for my midterm tomorrow. If you administered an online class I could do it in a few weeks.. You're incredible!
sir ur teaching style is just awesome... and ur writing is also very gud ,,,,,.....u rock sir!!!!!!!!
Thanks dude whenever an exam is coming up and I need to relearn some material you're always there to help! Thanks!
im impressed, our teacher taught us this in 45 minutes and i didnt understand a thing, and u explained this in 7 minutes and i understood it all :)
wow , you explain things so well, I wish my professors knew how to do this.. it's so frustrating going to all of my classes and being confused throughout the entire lecture. im a slow learner so i dont catch on like everyone else. you have a new subscriber! thanx
FlowerRFabulous same, but we're not slow learners, we just learn in different ways.
I haven't seen integral notation before, I was taught to write it as: {xER|x=/=-1/2,1/3,0}. Meaning x is an Element of the Real numbers and cannot equal -1/2, 1/3, or 0. Nice video :)
Even when U have 3 brain cells and doing my math homework at midnight, this is better than my teacher. Thanks so much!
Happy to help!
This is the only video I've seen of this guy, and I've already hit "Subscribe." YOUR VIDEOS ARE SUPERIOR. YOU SHOULD BE VERIFIED ON UA-cam FOR BEING SO AMAZING
Thank you!!! I've been trying a bunch of other videos and this is the only one I could understand!
This is amazing. It's quite easy to understand. My sister actually asks me for help about this stuff but I couldn't remember much about functions anymorr so I did some research and happen to find your youtube video. After watching your video I would gladly share the link to her because it's really informative and easy to understand. ❤😊✌
I was stuck on this and you made the light bulb come on! Thank you so much!
Was stuck on that common mistake of not checking the domain of the input function, thanks for the help! Cool channel
you help me more in an 8 minute video than my teacher in a weeks worth of classes..
amazing video! Really set my basics right!. Thank you! Can't believe that this 10 year old video would help me out so much!!!!!
@roseheroine no problem, happy to help!
@ploik21 interval notation, not integral. what you are using is called set notation. both work! : )
You have no idea how much this has helpd me. Thank you very much!!!!!!
You are an amazing person!
Thank you again sir!
omg thank you so much! i'm in precalc this year and had geometry last year and i could not for the life of me remember how to do this! you were awesome at explaining it, thank you so much!!!
Thanks! Extremely useful! My lecturer was going though this so quickly.
Thank you for going over the different types of notations, it means a lot!
come back any time :)
Thank you. This explanation was very helpful and now I'm not more confused.
I never see this type teaching on youtube good sir
I am so grateful for this, thank you so much!
I always forgot to take the domain of the inside functions. Thank you
This was a great video. Thanks for posting this, and keep more videos about pre-calculus or calculus coming please!
Thank you you are perfect teacher 👨🏫😍❤️❤️
This was 12 years ago but it's still very helpful
VERY helpful, thank you! I understood the composition of functions, but could not understand how to find the domains.
thank you so much i was really confused since the teacher explained it in class but i was very tired that class and she made us stand up to watch what shes doing on the whiteboard (so i was more focused on my legs hurting cuz we stand up pretty much the whole class its kinda annoying idk why we have desks at that point) so i tried to check canvas if she wrote ANY information about how to do this and she didn't so anyway thank you so much
you explain in better than the texbooks which cost hundreds of dollars and can't do much.
Is it the same if I use comma sign instead of union sign to express the domain?
I think the domain should be {x/x not equal to -1/2 u 1/3} 0 is not included. Because if you replace x with zero in the denominator the answer would be -6. This is only my opinion feel free to correct me if I am wrong :)
when you plug in 0 in the denominator you would get 1/0, which is undefined, that's why 0 is not included in the domain.
I am really satisfied.this is clear and easy to understand..thank you hei
Thank you so much for the well explained lessons! Your page is definitely an invaluable source of information!
Great work. Was good for just quickly confirming what I thought was the process for these sorts of questions.
perfect xplanation and perfect video quality!!!!!!!!!!!
Question: I notice that the domain restrictions of f(x) can be found by simply looking at the g(f(x)) equation. Is this merely a coincidence, or will it always be the case?
I noticed this too, for instance:
f(x) = 1 / (1 - x), g(x) = (x - 1) / (x + 1)
g(f(x))
.
.
.
= ((2 - x) / (x - 1))((x - 1) / x))
= (2 - x) / x, for x 1 since (x -1) / (x - 1) is 1
Domain is therefore x 0, 1.
Here, I determined that the domain of the composition can't include 1 without looking at the "inside" function f (although it was more work.)
The reason for this is that sometimes when you simplify, you "miss" a number that would otherwise have been excluded.
For example, say we have g(x)=1/x and f(x)=1/(x-4).
If we compose and simplify g(f(x))=1/(1/(x-4))=x-4.
Notice that this simplified version of g(f(x)) has no domain restrictions.
However, before we simplified it, we still have the domain restriction x=/=4.
Sometimes this matters, sometimes it doesn't. It depends on the context on the problem, but, it's always better to be safe than sorry!
Finally I get it! Was starting to feel really dumb. Thanks for posting
When it comes to interval notation of the domain, wouldn't it be more clearer to write:
R\{-1/2,0,1/3}?
It means the same thing, just in a less tedious format as opposed to naming all the four intervals between those values.
Just some constructive criticism, aside from that: good video!
+Natalie Elizabeth That would make it set notation. Not interval notation. So if the question asks for you to put in interval notation then you may not get the mark.
Thank you very MUCH!!! this video will help me a lot!!! i'll sit for my exam on this nov 2nd..... TQ Mr,,,, :")
Fantastic explanation. Hope more such video will get soon.
Thanks, very clear and helpful!
math quiz today! this is going to help me!
Can you explain to me again, how if you plug in -1/2 and 1/3 in the denominator, it’ll equal to 0?
yes I have this question as well
Kyra H ok so if you plug in 1/3 with the negative 3 parenthesis, you get 0 so anything multiplied with 0 gets u undefined
i find it quite interesting that he writes right to left sometimes... kinda dope
Excellent explaining, thank you so much!
Thanks dude, much clearer to me now. :)
@TheBarneyrubble08 no problem, come back any time
Great explanation
So clear thank you!
I love your voice LOL, it makes math easy
So the domain of f (x) woun't be included with the domain of (fog)(x) ?
So the domain of (fog)(x) would be from negative inifinty to positive infinity exept the zeros of the input function -in the this case g (x)- and the zeros of (fog)(x), right?
*So the domain of f (x) has nothing to do with all this, meaning I don't have to exclude it's zeros from the domain of (fog)(x), right?
2020 quarantine anyone?
Thank you this was so helpful!
thank you so much man this is helpful !!!
how would you find the inverse of f(x,y)=(2y-x,x+y) for f: R^2 => R^2,
I found your video very helpful but i still cant figure out how to do the question above,
Could you help me?
Should we really exclude 0? First our x=0 will go to g (x) and woun't be a problem, will it?
omfg thank you so much, i finally understand this.
good explanation and thanks sir
@DehXable yes, i know
thank you soo much Patrick!
thank you so much!! you helped me a lot!
my teacher aint even taught us this he just gave us homework on it
If you look at the rule: "range of inside must be contained within domain of outside" this function is not defined, so it probably was not a very good example, as it could confuse some people. Just a friendly warning!
this was amazing, thank you!
You're just fantastic. I hope you know.
Teacher videos always have to lowest audio lmao
I'm a little unclear how X can be equal to two different values within the same argument. -1/2 and 1/3 at the same time. I can see it if you were talking about a curve on a graph where it crosses the X axis in two places.
no that means x must not be 1/3 and 1/2
no it means that it can't equal to 1/3, nor can it equal to -1/2
I'm left handed too!
And thanks :)
This is helpful. Thank you.
thx man it really helped.
perfect!
very helpful thank you so much
would you download video have this example of composition :
f(x) = 1+x / 1-x , g(x) = x / 1-x
find fog(x) and gof(x) and find their domains
if you solve it i will be so happy :)
**i hope that you solve this equation as soon as possible**
you are amazing! thank you!
I understand the steps but can anyone explain why you don't simplify the equation before you find the domain?
Simple, if you simplify the equation before finding the domain, there is a possibility of a zero(or any number that would make the equation invalid) being included in the equation when it should be excluded because it makes the equation invalid.
its easier to find d&r if you don't simplify
Very helpful!
I love mathematics 100%
Why did you cross multiply? My mind is skipping that part for some reason.
soo helpful. thank you
Thank youuuu
ty bestie
thank you
what would be the graph of composite function look like anyone...please answer
thanks for your help
great video!!! thanks!!!
don't you also have to find the domain of g(x)?
Nice, thanks.