Functional Equations #1 - The Substitution Strategy

Solving a math Olympiad functional equation using the substitution strategy.

[kaiserquasar]

Oh dear Lord, your channel is EXACTLY what I needed to find. Thank you so much for this, I'll be bingingnthis series and taking extensive notes prepping for math olympiads. Hope to see y'all at the IMO!

[MatematicasNuevoLeon]

Great videos... I'll be recommending your channel to my students. You deserve more subscribers. 😎✌️ Greets from Nuevo León, México.

[judestjude]

Great explanation, thank you! I'm just starting out with functional equations, and this was the perfect introduction.

[bebarshossny]

this channel is golden
deserves more subs
glad i found you man thank you for these videos

[marienoelleseifasskar]

The function satisfies the equation and both sides equal 1+xy-y
Thank you so much great lecture please continue

[sr.tarsaimsingh]

Great,
You have so much patience to solve it by this, method. 🙏🏻

[brahdavv]

Make more of these amazing content please!!!

[Alevel_Physics]

Thank you very much man, need to prepare for a math Olympiad and this is very helpful

[ujwalmantri]

Yes the solution satisfies the functional equation
We get 1-y+xy of both sides

[gaetanolaudando]

So good, thank you for this kind of videos, they are really helpful, Italy.

[avyakthaachar.]

Thanks a ton for this video series! Very helpful 🙏❤️

[trip.]

Thx for this!!! Greats from Fortaleza - CE/ Brazil.

[johnmelis]

Wow awesome problem thank you for making these videos!

[martyshyu]

Checked and yes, the solution is correct.

[peterdriscoll]

How could you analyze a functional equation such as Euler's reflection formula, or Riemann's functional equation? Do these functional equations define a unique function? How do we know when a functional equation defines a unique function?

[anon_commentator]

Листаю задачки, и это очень хороший самоучитель. Сами задачи интересные, я раньше таких не видел. И вы объясняете хорошо несмотря на то, что я плохо знаю английский. Буду рекомендовать друзьям ботающим функциональные уравнения.

С любовью, из России

[souravpaul]

Really, really, great lecture,
thank you so much, sir🥰🧡

[strigibird]

In the step where you conclude that 1=f(f(y))+f(y). Would it be possible to make a substitution such that u=f(y)? Which would make the equation 1=f(u)+u. This can then be rearranged to become f(u)=1-u.

[garvittiwaria]

Really great lecture thank you so much

[spiderjerusalem]

Any prerequisite to Titu's functional equation? He had quite many typo's and his way of conveying ideas often gives me headache by reading it