Functional Equation

In this video, I showed how tosolve a functional equation

[WhiteGandalfs]

He is a very patient teacher with a very sympathic voice and charisma.

[VictorGarcia-gvri]

I love you're enthusiasm. It makes me feel like I'm not crazy or left alone because sometimes I find math or science fascinating and when I try to talk to people about it they look at me weird. We need more teachers like you.

[paulw]

hey, I'm 65 and just starting to do some math again. I was able to follow that long forgotten algebra so thanks, that is encouraging - subscribed.

[malefetsanekoalane]

I am a pensioner and I alternate between doing math and the garden.Your presentation is just so captivating. I just can't imagine what I would be doing if I couldn't do math .Kudos from Johannesburg. Been thinking that functional equations were reserved for IMOs. 😅

[sophisticatedplayer]

10:55 The top part was a perfect square, you don't even need to distribute everything
((t + 1) + (t - 1))^2 = (2t + 1 - 1)^2 = (2t)^2 = 4t^2

[johnconrardy]

i am 70 retired eng;ineer you got my attention love your teaching style and i love math

[MervynRThomas]

I love the fun you have with maths. Your enthusiasm is infectious. I wish my teachers had had half your ability.

[nihadsaid]

انا من فلسطين . واحب الرياضيات . انت مذهل و رائع . ساتابعك باستمرار . تحياتي

[selahattinkara-oh]

This teacher of ours; Eagle-eyed and confident. He displays body language according to the students' level of understanding. He gives wonderful and super lessons. He is a complete math genius.🌺👏

[zk]

Functional equations were always very cruel to me. Thanks to you, I'm starting to see the light. Keep on teaching!

[yamada.masahiro]

Your way of solving it is universal. Great!
I found the numerator of RHS equals ( x + 2 )^2, and then I tried to express the denominator with ( x + 2) and ( x - 2 ).
8 x = ( x + 2 )^2 - ( x - 2 )^2
∴ RHS = ( x + 2 )^2 ÷ { ( x + 2 )^2 - ( x - 2 )^2 }
= { ( x + 2 ) / ( x - 2 ) }^2 ÷ [ { ( x + 2 ) / ( x - 2 ) }^2 - 1 ]
Replace ( x + 2 ) / ( x - 2 ) with x, you can get x^2 / ( x^2 - 1 )

[IRanOutOfPhrases]

Been WAAAAY too long since I looked at this stuff. I was always pretty good and keen on math, but once this stuff started to turn up, it made the subject loads more interesting. It's hard to describe, but the way these functions relate to one another, it almost feels like you're peeling away at the layers of how the universe as a whole operates.

Some of the discoveries end up being more exciting than others, of course. Very similar vibes with how taking the derivative of a function, and then taking that derivative, and then taking that derivative, and all these functions you end up with all relate to one another. It's like the numbers behind the numbers behind the numbers.

You're introduced to things like parabolas and other common graph shapes well before learning derivatives, so it just felt like a huge plot twist when you first learn that these derivatives were there 'driving' the shapes of the graph all along. I don't know, just always seemed very cool to me.

[labbertubes]

this is one of the most compelling math videos it has been my joy to behold. Nice cap, too.

[favourtube]

I am from Bangladesh. And mymother langyage is not english. But your lecture is incredible. Despite being a bangali i can understand your solution so easily.your way of teaching is not boring at all. You are a really great teacher

[marxcarton]

This is where i learnt how to solve functional equations, thank you so much!!

[Zombie_Chess]

that's amazing. Never seen functional equations before but solving that looked like a lot of fun.

[gooddude]

Excellent sir. Loved the way you simplified and great explanation.

[matthewkendall]

Neat algebra - you might wish to explain how the original function won't given an answer at x = 2, whereas the revised function won't give an answer at x = 1 or -1 and how that works okay - as you have shifted the points where the function doesn't converge because of a divide by zero and why that would be allowed!

[freddyalvaradamaranon]

Muy interesante, didáctica y buena clase, a mi hija le servirá mucho esta excelente exposición. Estamos muy agradecidos con su bella persona, bendiciones y éxitos para Usted y su linda familia. ❤

[subarnodatta]

Sir I am an Indian student studying in class 12th (high school)..

i substituted t = x+2/x-2, and then directly used COMPONENDO-DIVIDENDO to get t+1/t-1 = x/2.. so x = 2(t+1/(t-1))..

then I directly considered (x^2 + 4x + 4)/8x as (x+2)^2/8x and substituted x as 2(t+1/(t-1)) on both the sides to get the desired answer.

Thanks a lot for this question sir..