Solving a Rational Functional Equation

This video is about solving a Functional Equation

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#ChallengingMathProblems #FunctionalEquations

EXPLORE:

[davidseed]

At 4:12 equation 2 is written incorrectly first term should be 1/(1-x)

[Justin-gkhu]

Can you do a video on how to solve functional equations in general or to solve different classes/types of functional equations please? Would be much appreicated as I find functional equations to be quite elegant.

[chillomillo]

2:55 I didn’t get it how you simplify the expression

[neuralwarp]

I love this. It's like magic out of Harry Potter.
"Specialis Revelio !"

[manojsurya]

Functional equations are also good, pls put next video on differential equation

[brunolevilevi]

I feel like this can be solved only because of the fact that f(x) = 1/1-x kinda repeats, f(f(x)) = f^-1(x) and f(f(f(x))) = x

[williamhogrider]

There are many ways to solve different functional equations... Many times you have to play with it for some time.

[joaquingutierrez]

Nice video !! I love how you solved it

[ahcenecanpos]

errors in f(1/(1-x))# f((1-x)/x) errors no simplfy

[spelunkerd]

Not doing this every day, I'm stumbling on why you are allowed to conveniently assign x=1/(1-x). Aren't you changing the parameters of the equation? If you do decide to do that, like a u-substitution for an integral, don't you have to change it back after you get it into form?

[Strohhutjunge]

At 3:43 the equation 2 is written wrongly, should be f( 1/(1-x) ) + f( (x-1)/x ) = 1/(1-x) . Please correct this or take video out!

[HakingMC]

By the way, from the first equation, how would you determine x≠1, or is it purely written down because you know from the final solution that x cannot be 1 for f(x) to be defined?

[AngadSingh-bvvn]

Matt Penn recently did this same functional equation on his channel.

[ezzaddin]

thank you for this strategy I will surely use it!

[chattemr]

Eq (1) +Eq(2) - Eq(3) does not cancel out 4 terms. Hence there is a serious flaw after this step.

[Joker-efkt]

Great video as always <3
How about this one from 1995 Russia Mathematical Olympiad:
Prove that the equation cos(cos(cos(cos(x)))) = sin(sin(sin(sin(x)))) has no real solutions at all

[muhammadsheyhidan]

I dunno how to do it and also dunno how did you come with that approach.. amazing 🤩

[sebastianramirezcaseres]

Thanks a lot ! Its a great channel.
Greetings from colombia 🙂

[generalvideos]

Substituting 1/(1-x) instead of x will not affect the

[comingshoon]

típico problema de olimpiadas de matemáticas, así como para soltar la mano jaja ... saludos desde Chile bro