Methods of Functional Equations

In this video, I showed how to solve functional equations using both substitution and form manipulation

[embracinglogic]

My friend, you are the best math channel on YT. In fact, you are better than 99% of math professors. Thank you.

[JosephChifamba]

Did uni math 39y ago (y85/86). Our professors would just write down so fast and we would copy and later teach ourselves evenings. I envy this tutor. The best there can be, simply the best!

[uzaytakip]

This guy was born to be a teacher; humble and yet commanding.

[ton_ak]

What a blessing this video showed up in my for you page. Not only you've been able to make me understand something I've never saw in school, but the energy and the passion you put in your lesson are inspiring. The pauses to let us think and absorb the conceps before moving on make the video perfect.
"Those who stop learning stop living" is now my life instructions

[jamesharmon]

Method 2 was so obvious once I saw it. I will never "freak out" again when I see problems of this type. Thank you!!

[manuelacosta]

You are an excellent teacher. It makes me remember 45 years ago a teacher I had like you. It is very nice to know that there are still people with your passion and soul for teaching..👏👏👏

[tmjcbs]

I did it with a slight variation of method 2: f(x) = f((x-1)+1) = (x-1)^2-3(x-1)+2 = x^2-5x+6.

[markTheWoodlands]

Consistently excellent work. Clear, concise and artful.

[williamspostoronnim]

Превосходно! Наконец-то вижу внятное объяснение, как решать функциональное уравнение.

[kumarkailasanathan]

Concept is made very clear. Love your teachings. Wish all students will make best use of teachings

[ThePhysicsTutor-hbiw]

Beautiful approach to the question. You are too good. The mistake that most students would have make was to substitute (x + 1) into the function x*2 - 3x + 2 which is a terrible idea.

[rafaelcueto]

Wow.... me encantó su forma de mostrar lo apasionante de las matemáticas y se siente lo mucho que las disfruta... me alegró de verdad... 😊

[dougaugustine]

These things have been frustrating me for awhile. But today while sitting in the bathtub, it finally hit me and I understood the simplicity of the concept using t substitution. The first method was a nice touch too but for now I will simply be happy for the imoment of realization.

[andrewlayton]

I appreciate that you start by asking very directly "What are we trying to find?"

[SanePerson]

Frankly, I solved this as basically a 'word analogy' problem: x + 1 is to x as x is to x – 1. Therefore, you can solve the problem most quickly by taking the expression for f(x + 1) and if you substitute 'x – 1' in that expression everywhere you see an 'x', then simplify, you have an expression for f(x). Of course, that's is no different than doing the 't substitution' at 6:00, but it saves a step and it seems intuitively easy.

[bhgtree]

You explain everything so well, I wish you were my teacher when I was in school (I am getting back into doing maths, hoping to do Calculus > analysis > abstract algebra etc).

[punditgi]

Master of teaching. That is Prime Newtons! 😊

[glorrin]

Sorry, I have been yelled at by my teachers so many times for not explicitly giving domain and range anytime I see a function, I now instinctively do it.

[tayebtchikou]

So I'm one of the masters😁 thank you so much for what are you doing for us in order to learn maths easily

[yoavmenuhin]

Man, i just love your passion so much, you have such a good feel for teaching l.
I'm literally feel safe when i watch your videos.
You are an inspiration and a blessing ❤️