Olympiad Challenge! Solve this function Equation | Easy & In-Depth Explanation

[GiuseppeAriano]

I took the following way: f(x) = x - f(1/(1-x)) = x - 1/(1-x) + f(1/(1-1/(1-x))) = x + 1/(x-1) + f((x-1) /x) = x + 1/(x-1) + (x-1)/x - f(1/(1-(x-1)/x)) = x + 1/(x-1) + (x-1)/x - f(x).
So, f(x) = x + 1/(x-1) + (x-1)/x - f(x).
The conclusion easily follows.
Thank you and compliments for your work, Sir. 👍

[wackojacko]

I remember a lot of the progression of learning when too use substitutions and then combining equations by adding or subtracting them. This problem for me, really reinforced the process for evaluating....thank you for posting tutorial.

[VSN]

Hello, thank you for such a great video. May I ask what motivates you to replace x with 1/(1-x)? Also, is there a unique property of 1/(1-x) such that x replace by 1/(1-x) followed by x replaced by (x-1)/x results in x again in f(x)? Thanks :)

[lnofzero]

You always present such a patient, excellent treatment of the puzzles!

[focusconsistency]

Been a while since solving functional equations!
Keep 'em shooting sir!
Kudos and Thanks!

[l.w.paradis]

Super! Love functional equations.
But how did you get the insight of where to start?

[math]

very well done, great job solving this function equation, thanks for sharing

[notAD]

Thank you sir! Because of you, I'm starting to find math interesting and sure am improving!

[mputuchimezie]

Please can all functional equations be solved using this approach?

[aztakademy]

I have trouble understanding your change of variable since you kept the same variable substitution.
Thank you for sharing.

[pranavamali]

Really helpful i want such more questions of function i want to practice them

[sotonkst]

Can use polynomial division to show x^3+14=(x^2+7x-2)(x-7) +51x. Since x^2+7x-2=0, x^3+14=51x. The answer 51 follows by division by x.

[rangaswamyks]

Its very defficult sir
You are great sir
I love you
As my master of maths

[arthurleaoteles]

Great video! I really enjoy the way u explain it! Keep it up!

[ramanivenkata]

Excellent. It doesn't occur to me to bring in an Extraneous
value to be assigned to ' x'.
👍👍

[Mathskylive]

cảm ơn, giải phương trình hàm bằng biến đổi hàm số.

[rahymjanjarbol]

Good afternoon! I drew up a drawing for the development of a mechanical gearbox, betraying comfort in the manipulation of the lever. it needs to be sold. Can you help?

[shreyanshbhanu]

Wohhaaa!! Solved by me... Within 4 minutes 🙌❤
Date :- 8th May 2022 1:23 AM

[gnyandevkshirsagar]

Excellent explaination any average student can understand

[gudyou-atul]

Wow sir thanku 🙏👍 but i puzzle into these questions