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!!!!

[@amaliacoughlan7071]

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

[@yaseenhoque2636]

yo this was the best video on proving a surjection

[@TheMathSorcerer]

thanks man

[@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 😄

[@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!

[@JesseBourretGheysen]

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

[@TheMathSorcerer]

Awesome !

[@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!

[@nayanakr]

Thank you sir, this video helps me a lot.

[@TheMathSorcerer]

Excellent!

[@minkihairoil]

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

[@cuberkahmin42]

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

[@TheMathSorcerer]

You're welcome!

[@luxtenebris764]

Sir you're da BEST thank you alot

[@TheMathSorcerer]

:)

[@a.human.]

Man you saved my life.

[@muhammadsaif4849]

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

[@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?

[@fredesl406]

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

[@marinajacobo3550]

Thank you! :)

[@TheMathSorcerer]

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

[@kuroshkabir136]

thank you very much

[@tn9711]

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

[@TheMathSorcerer]

Lol

[@TheMathSorcerer]

Good luck 👍

[@marcoventura9451]

Very good!

[@Aisyah-qf2pz]

Thank you.

[@HasanItani-d8b]

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.

[@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?

[@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.

[@omarr993]

i love u

[@martinhazard2025]

Wrong, very bad explanation