How to Prove the Rational Function f(x) = 1/(x - 2) is Surjective(Onto) using the Definition

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How to Prove the Rational Function f(x) = 1/(x - 2) is Surjective(Onto) using the Definition

[@3hazit7]

This is the best example I've seen on how to prove a function is surjective. Thank you! Helped a lot.

[@TheMathSorcerer]

glad it helped!!!!

[@yaseenhoque2636]

yo this was the best video on proving a surjection

[@TheMathSorcerer]

thanks man

[@amaliacoughlan7071]

Math wizard is really out here saving lives. Thank you!

[@ananddeeznutzjohncena1711]

literally, no one else actually explains it. they just say its surjective because all y can be achieved via the subset of x values. yes but if I write that when my professor asks for a proof I will be failing the course. Thank you for ACTUALLY providing the proof and method.

[@mostafamahtab7349]

I just copied it in my cheat sheet

[@sophiabnrm8730]

This is incredible. Have not found anything similar to your explanation. I found almost no useful tutorials on this topic - EXCEPT THIS ONE! Your work is very much appreciated and I thank you very much for your time and energy, that you put into this videos. I hope you have a few videos on injective as well, since it is part of characteristics of functions as well! Wish you all the best! You gained a need subscriber

[@TheMathSorcerer]

Thank you!! I do check my playlist on functions. Scroll down from the main page 😄

[@JesseBourretGheysen]

This helped me with my set theory homework a Ton. Going to subscribe to your channel. A genuine Math Sorcerer!

[@TheMathSorcerer]

Awesome !

[@ld8162]

You are totally math sorcerer. I love your films! Its easy to see, that you are real enthusiast of the math! Its nice to watching you because of that, and you can clearly show theory and examples. Greetings! :D

[@TheMathSorcerer]

thank you and greetings:)

[@ld8162]

@@TheMathSorcerer I'm math student, and youre very helpful :)

[@TheMathSorcerer]

@@ld8162 awesome!!

[@ld8162]

@@TheMathSorcerer Yeah! I love my study, but sometimes its hard :D Especially at first year. But for math everything :D

[@boiplaying2647]

i actually got surprised for a second, seems like you gave me some interest of maths back, The university teacher is speaking like a i have a doctorate in maths

[@TheMathSorcerer]

yeah math is awesome man!

[@ado4224]

Great stuff. I always tried to prove it with limits and getting +/- infinity, but this is way better for not messing something up when calculating.

[@aniketmukhopadhyay8962]

Thank You So much for this Video!!!!!!! This helped me a lot!

[@cuberkahmin42]

thanks, this video is the best of proving a surjective , :)

[@TheMathSorcerer]

You're welcome!

[@nayanakr]

Thank you sir, this video helps me a lot.

[@TheMathSorcerer]

Excellent!

[@dv4346]

Man no matter how many videos I watch or how hard I try I don't get it. Well made video but I didn't get it still- not your fault though! Ig I just need to switch majors haha

[@luxtenebris764]

Sir you're da BEST thank you alot

[@TheMathSorcerer]

:)

[@a.human.]

Man you saved my life.

[@flashgames1273]

if we take f: R\{2} -> R, this means that the function is not surjective and therefore it can't have an inverse function?

[@marinajacobo3550]

Thank you! :)

[@TheMathSorcerer]

no problem, I am happy that this helped someone:)

[@Aisyah-qf2pz]

Thank you.

[@tn9711]

Every proof looks simple and intuitive until I try to solve one 💀

[@TheMathSorcerer]

Lol

[@TheMathSorcerer]

Good luck 👍

[@kuroshkabir136]

thank you very much

[@muhammadsaif4849]

Please give me a example of function that is surjective for f:z×z >R

[@marcoventura9451]

Very good!

[@fredesl406]

has anyone ever told you you look like jeff bezos with hair?

[@shindayuza6456]

I used this method and somehow was able to prove that x^2 - x is surjective, when I know it isn't, why is that?

[@omarr993]

i love u

[@ScilexGuitar]

Is this a legit proof tho. I thought we cant assume f(x) = y in the start

[@ArushMangal-hm6rx]

He didnt assume f(x)=y, he took an arbitrary number y from the Codomain of the function which he then proved always belongs to the range of the function as well. Doing that, he has effectively proved that Range which can only be a subset of the Codomain is actually exactly equal to the Range (since every element in the codomain is equal to another in the range), hence proving that the function is onto/surjective by definition.

[@user-hr4xi3qn7j]

why we didnt expand y(x-2)

[@jasonle7522]

Since he solving for x you want to isolate each variable. if you attempt to expand then you would get 1 = xy-2x but at this point it wouldn't be possible to solve for x.

[@martinhazard5982]

Wrong, very bad explanation