THANK YOU!!! All the other videos on here only talked about how to prove a function is surjective, and not how to use it’s properties to solve problems. This really helped me
Thank you for making functional equation making easily understandable for me. I am not in high school but i like these kind of problems. Though hard for me,but i am doing more and more of these. _Subscribed_
Hey bro, keep going. 👍👍👍. Functional equations were a nightmare for me. But now I am understanding the physical aspect of it. Lots of love and support.
If anyone else was confused like I was at first about why fff(x)=ff(x) requires f to be surjective to solve, here's what I figured: Because x≠x²/x at x=0, if f isn't surjective, x²/x is a solution. Hence we need to find out if f is surjective to prove that f(x)=x is the only function. I'm not sure if this is really the case tho 😂
@@littlefermat Alright thanks for the quick reply also when we assume a number alpha such that f(alpha)= smth can we assume an another numbeer beta f(beta)= smth2 ?
@@debayuchakraborti1963 No. Right now they are exclusively on Michael Penn’s channel and I consider moving then on my own channel some day in the future
THANK YOU!!! All the other videos on here only talked about how to prove a function is surjective, and not how to use it’s properties to solve problems. This really helped me
@@Mewhenthewhenthe-x7j glad you liked the video, the whole playlist is discussing techniques to solve functional equations.
@@littlefermatAwesome
This is very good, soon you'll have more subscribers, keep going
Thank you for making functional equation making easily understandable for me. I am not in high school but i like these kind of problems. Though hard for me,but i am doing more and more of these.
_Subscribed_
You are welcome my friend!
Hey bro, keep going. 👍👍👍. Functional equations were a nightmare for me. But now I am understanding the physical aspect of it. Lots of love and support.
Glad to hear that!
Thank you. This was a nice trick. I'm glad I solved it, but I wouldn't have been able to if I didn't think about surjectivity. Great videos as alwats
hi
If anyone else was confused like I was at first about why fff(x)=ff(x) requires f to be surjective to solve, here's what I figured:
Because x≠x²/x at x=0, if f isn't surjective, x²/x is a solution. Hence we need to find out if f is surjective to prove that f(x)=x is the only function.
I'm not sure if this is really the case tho 😂
I know I am 3 years late(but tbh idc). If f doesnt have to be surjective, we could just substitute f(x)=c, where c is some constant for example
That was awesome!, thank you and keep it up!
These videos are great
Good one Mohammad thanks.
Nice one! Adding this subjectivity lemma to my Notes.
Edit: *Subjective* not *Surjective* xD
it's surjective, lol
Great video, thanks!
Awesome.
Where are you from?
Wonderful ❤
Great Video! I didn't understand how you check if the result is correct...
if
f(f(y))=y and f is surjective does that also mean f(y)=y?
@@Marlow998 If f(f(y)) =y then f is already surjective as f takes all values. Of course that doesn't mean f(y) =y. Take f(y) =1-y as a counter example
@@littlefermat Alright thanks for the quick reply
also when we assume a number alpha such that f(alpha)= smth can we assume an another numbeer beta f(beta)= smth2 ?
Only if f is not constant (except for 0 and 1 as constants) and if that smth2 is in the codomain of f (I suppose)
Do we not need injectivity to do that?
No, surjectivity here is enough to crack the fe!
Thanks sir
10:58
Omg u r here
@@debayuchakraborti1963 Yeah that’s me 😎
@@goodplacetostop2973 so r u going to post hw problem here too :P
@@debayuchakraborti1963 No. Right now they are exclusively on Michael Penn’s channel and I consider moving then on my own channel some day in the future
@@goodplacetostop2973 :thumbsup: