Every function can be written as sum of one even and one odd functions (CSP 7)

I give a derivation and also some examples of how to apply this fact

[@tommyvanluchem8788]

Very good video, helped me lots with my uni :) Greetings from Belgium

[@SBMGerman]

Hello Tommy and thank you. I am happy, that it helped you. Greetings from Dusseldorf

[@bangprob]

Thanks

[@SBMGerman]

Happy New Year!

[@rheasingh8716]

Thank you for the video, it was very helpful. I do have a question though. Can f(x)=x^2/3 + x^1/3 +1 be written as a sum of even and odd functions? Or because the exponents aren't fractions it cannot be?

[@SBMGerman]

Hello and thank you! Sure. Look, X*2/3+1 is an even Part and X*1/3 is an odd öne. Got it?

[@ingemeyer3627]

Hi, why did you decide to add f(x) + f(-x) at 6:56 ? I understand that that helps us get to the needed equation, but how do we know that that is what we need to do?

[@SBMGerman]

Hello! Well, İ am doing something in order to prove the given result. Since I am not assuming anything wrong, the follow up is legal. You can consider it, as picking the right key to open the door. I could have tried more approaches, whick wouldn't have worked out and then come up with something, that works. Giving the result , which is working in this case is the only way to make it a watchable KZbin video

[@ingemeyer3627]

@@SBMGerman so it's usually a kind of trial and error situation? But since we already know the approach works for this specific proof we can just use it?

[@SBMGerman]

This is exactly the way. İt is overwhelming at the beginning, but during the study time you will figure out, that there are some packages of needed and basic technics and something outside of tho box is causing troubles not only for you, but also even for professionals, with way deeper background and much experience. So, stay tuned!