One-to-One and Onto Functions

[@animallover4ever100]

If I had this teacher, I'd never miss a class.

[@NicholasJMV1981]

thanks for the love. I'm blushing!

[@yootantonystark2738]

animallover4ever100 If i had you as my teacher...well, i'll probably drop out! jk jk

[@beanhumann]

Hahahha, sameeee😍

[@imnotayoutuber7781]

S I M P

[@mikethanks2299]

It's amazing how in 7 min you were able to explain something that teacher struggle to explain in hours. Thank you for the video!

[@NicholasJMV1981]

Mike Thanks Thank you Mike! I hope it helped!

[@Dvidseidl]

I am currently studying Economics at University, I understand all the complicated stuff but not those simple things and all explanations that I found on this subject are so incomprehensible. Thank you very much for making it this simple !!! ( Because that's the Art of Explaining: To make it as simple as possible, but most of the teachers (and University professors) can't understand that... Again, thanks !

[@NicholasJMV1981]

thank you so much! I really appreciate it

[@TheHalcyonAnon]

You explained in 20 seconds what four books, a tutor, six other videos, Khan Academy, and a professor could not. Thank you.

[@TheBlackAmericana]

Pretty Handsome Math teacher....

[@TarunArora01]

Thanks for this information. Even being 6 Years to this upload. This is helping a lot of students in getting clarity. Cheers.

[@mekings0422]

i have exams this morning and with this i am very very good to go... thanks so much sir

[@dhruvnainwal8457]

Great topic completed in 6 min,,, appreciable

[@aaronz5072]

Your explanation is pretty clear.Thank you for your time.

[@swlau4161]

Very good and clear explanation! It will be good if you can also list an example of an onto function but not one-one, such as f(x) = x^3 -2x^2+7

[@NicholasJMV1981]

Thank you so much for watching. If f(x)=e^x, the function is not onto because not all y-values are mapped from a value in the domain (for example 0).

[@LVLTM]

Your videos teach more succinctly than any university professor I've had. +1!

[@NicholasJMV1981]

Thank you!

[@Kernviter]

This guy saved my life in discrete math class

[@malliswarireddy3329]

Explained very well. Thank you for covering these topics.

[@NicholasJMV1981]

Glad it was helpful!

[@NicholasJMV1981]

Made a mistake with x^2+2. The function is onto since all the y-values (codomain) have an x-value that "goes to or maps to it."

[@leftfieldhero]

So does that also apply to the absolute value function?

[@austinmitchell2652]

This would be a great comment to pin!

[@kinggeedora]

what about the negative y values?

[@jenkinsj9224]

@@kinggeedora they are not in codomain

[@sadeepapiyumalranasinghe7128]

simply and nicely explained.highly recommended video

[@Gary1q2]

u r a fuking legend m8

[@NicholasJMV1981]

+Gary1q2 Thanks buddy

[@ganeshps100]

wow. You cleared all my doubts about one one and onto. Thanks a lot.

[@Movieplanethub]

Nice explain Sir

[@kaveetajain9051]

Thank you so much for this video...really helped me

[@NicholasJMV1981]

I'm so glad!

[@charlesamofordjuoh9940]

I really love your videos, even though you dont get plenty of views please keep on doing them

[@NicholasJMV1981]

Thank you. If any of my videos help you then I have done my job!

[@banjoowo4001]

he has now 197k views..thats a lot

[@sci-star5085]

This is such a great and simple explaination 👍💛

[@gustavomarquesdasilva1167]

Came here to learn maths and felt in love

[@NicholasJMV1981]

+Gustavo Marques da Silva Thanks for the love

[@deepalilondhe8541]

Appreciated man ur sharing ur knowledge in this evil world..

[@NicholasJMV1981]

Anytime

[@NicholasJMV1981]

no problem

[@mr.yanlucena8463]

Thanks, Nick. Very explanatory video.

[@Sezetcik]

Quick and clear explanation, thank you

[@ivankontra3446]

Can't believe I had to google this in English. And it worked.

[@KartikKumar-np5ch]

Really interesting and Good teaching method

[@ariellalee4749]

You're a great teacher, thank you for your videos!

[@St_Samuel]

this vid helped me in my linear algebra class :) tnx so much

[@amjadmounajed6653]

Thats what i call real explanation 👑👑👑 just one question to be sure ...for a function to be onto should its range ALWAYS cover -infinity to +infinity? Thanks 👍👍

[@amazingmanish]

Very well explained . Good Job.

[@dibasacharya9347]

Cleared the confusion and helped in my exam.Thank-you Very Very much

[@coachbennett10s]

Glad I could help

[@AmalaChristyDaniel]

Superb!Way to go.!I need the explanation of the difference between one one and into function.

[@kevingibbs5341]

Wow! that was all explained so amazingly well!

[@jenojosephinmariya317]

the best

[@komal_rangoonwala]

Extremely well explained Nicholas! thank you very much :)

[@punksnotdead4766]

Thanks for this. Really cleared up difference between the two types for me

[@suryanshsingh4114]

Ohkk thanks sir... I got it...🥳 Well..I'm from India🤗

[@learntoearn6612]

This guy is very smart too 👌

[@andreischannel4594]

Thank you so much for explaining it in such a simple manner! Instead of explaining it as simply as you do, my teachers give such long definitions that make all the students do mental gymnastics and leave them confused. Instead of saying in one clear sentence that two values of x cannot be assigned to the same output for one-to-one, I receive explanations in class such as: A function fis said to be one-to-oneor injectiveif and only if f(a) = f(b) impliesa= bfor all aand bin the domain of f. A function is said to be an injection if it is one-to-one.Alternatively, a function fis one-to-one if f (a) ¹f (b) whenever a ¹bUsing quantifiers:"a "b (f(a) = f(b) ®a= b) or "a "b (a¹b®f(a) ¹f(b) ) WTFFFFFFFFF

[@satadhi]

absolute legend dude !

[@orapelengbawa9180]

Thanks a lot Nic, this was very helpful man. Appreciated.

[@NicholasJMV1981]

My pleasure! Glad I could help

[@prithishroy_01]

I loved it... Thank you sir for your explanations 😊😊

[@greenElement]

Why can't professors be this clear IRL

[@NicholasJMV1981]

+GreenAlpha Thank you! I do my best

[@devenpatel9358]

Nice one and simple Thank you

[@NicholasJMV1981]

Glad you liked it

[@austinmitchell2652]

Excellent explanation, thank you so much!

[@Emzo.Magazine]

simple and useful. Thank you

[@allydimoso939]

fantastic presentation

[@NicholasJMV1981]

thank you Ally!

[@gaicheng1992]

Fantastic video. Thank you so much.

[@NicholasJMV1981]

+Gai Cheng Glad I could help

[@sanaseethevan5538]

hello sir your explanation is superb

[@kedarkelkar4350]

Thank you very much for this explanation.

[@NicholasJMV1981]

+Kedar Kelkar anytime!

[@isaacfoncha7123]

Awesome! I like your explanation.

[@NicholasJMV1981]

Glad to hear that!

[@nirupamam2814]

He should have been my teacher forever

[@sushantgharal6749]

sir your video really helped.....please make a video on ghrafs of different funtns.....thankyou sir

[@spaceboy2099]

great explanation, helped me a lot! thanks!

[@mekings0422]

wow.. just wow... amazing

[@webbyspidey]

Thank you so much Nicolas for helping me visualize things with the help of graphs. I was able to understand the concept. But I have a doubt. Can one domain (x-value) have two codomains (y-values) in an onto function?

[@coachbennett10s]

+Vrusha Dhwaj Glad I could help

[@tinhhuynh2641]

+Vrusha Dhwaj yeah, as long as there is no y-value that isn't paired with any x-value

[@notanatheist1248]

Yes, using the "ONTO" designation, but that of course would not actually be a function.

[@afreenyousaf2104]

thanks alot.it helped . it saved my finalssssssssssssss..

[@YasirKhan-ch7ih]

This video was really helpful.....I appreciate the work...Thanks buddy 😀😊👍

[@NicholasJMV1981]

My pleasure!

[@sdvsdv4833]

Thanks a lot.. Love from India 😍

[@NicholasJMV1981]

Thank you too!

[@jayceinfinitealgharhythmns9814]

I was looking for the algebraic equation as well for f(x)=3x-4, even though I should know it, I was hoping for a more complete explanation!

[@mikekafei]

Thank you! Very concise!

[@NicholasJMV1981]

thanks

[@NabaaYousif0_1]

Thank you for this helpful video

[@strongapple3031]

This video is very helpful!!!

[@NicholasJMV1981]

Alinaddung glad you liked it

[@nobodydance007]

After watching this video, I got a better understanding rather reading a textbook.

[@NicholasJMV1981]

Jason Situ Thank Jason, glad I could help!

[@mch8906]

Thank you man, I have an exam tomorrow and this helped a lot.

[@NicholasJMV1981]

+Moham'mad Sha'aban How did you do?

[@mch8906]

Really good. Thx.

[@thabisongwane2]

Well explained ey. could you please upload a video that shows how to determine Function if is onto or one to one without using try and error method

[@osamazahid8922]

Amazing stuff man!! Really helped me out there! Thanks a bunch!! :)

[@kellyk2215]

you are amazing. are great at explaining thank you

[@coachbennett10s]

+kelly persaud Thank you Kelly!

[@doktoren99]

Really good explaination sur. But i wonder, is there a way to prove that the parable funciton is not injective by using algebra?

[@NicholasJMV1981]

I would have to look in to this

[@rakshajain6773]

thanks sir. :D supremely helpful!

[@shivikaagrawal7246]

could you please tell how is the given que an onto function. Que: f : R --> R f(x) = 2x My doubt is that since range contains all the even values(i.e. no odd ones will attain their pre image).. so how is it an onto function?

[@MSH3423]

f(x)= ⌈x/7⌉ -5 This Function looks like linear function but there steps in between.. will this be consider One to one ( for all x values there is link to one Y value...) but some X values share same Y value...

[@usmankhokhar8083]

great effort learn alot thanx

[@stefanmarjanovic4768]

very simple and easy to understand

[@NicholasJMV1981]

thanks

[@MysteryofScience]

thqnk you sir you are good teacher

[@AkshayPhilip]

sir in case where all values in range is paired with single domian value , and there is few elements is floating in domain which is not paired with range , is it a one to one function ?

[@naveedmirani3202]

Your video helped me so much 😀👍

[@NicholasJMV1981]

+Naveed Mirani Glad it did!

[@muhammadanwar-ul-mustafa7696]

thank you sir! for that worthy help but i have a query that what should be the solution for a function_ f(m,n)=2m-n.... is the function an ONto function ... if it is then how it is??

[@NicholasJMV1981]

Let me get back to you. I can check

[@zhinaaziz8009]

I was getting confused in discrete matthmatic thank you so much

[@NicholasJMV1981]

No probblem!

[@yasssh7835]

awesome man...good work keep it uo

[@milindkale8498]

thanks for great teaching

[@NicholasJMV1981]

+omkar kale Appreciate it!

[@terminatortscc1]

I appreciate your help, thanks sir!

[@coachbennett10s]

Thank you!

[@natyjerky6300]

Kept it simple and interesting, awesome man😍

[@NicholasJMV1981]

Thank you!

[@sreenivasareddy2285]

It was really useful Ty!!!

[@ElkePoN]

this is also discrete math, do you have tutorials? I'm taking it now :)

[@jtjuan7]

Wow, great explanation, thank you!

[@NicholasJMV1981]

Thank you so much. Sorry for the late reply, comments were not showing up here.

[@user-nf5qt6yc7p]

saved me from talking to my hard-to-understand discrete maths teacher, thnx

[@NightlyShadow]

Does this mean that unless the range is (-infinity, infinity), the function is not onto?

[@SidharthShambu]

I'm like number 1000!

[@harishmanoharan173]

Very helpful!

[@t12m99]

does range have to be. (-infinity,infinity) for a function to be "onto"

[@sewdanesre730]

you are super teacher

[@mayankcharan1688]

thank u soo much it helps me a lot......

[@logicthat5591]

better than my professor

[@anthonysenju4044]

Great lesson.

[@NicholasJMV1981]

thank you!

[@monicajeanbusog8357]

I've learned that a linear equation is always a bijective, while quadratic equation cannot be one to one most probably cannot be onto. is there any other easy way to determined whether the equation is injective, surjective, and bijective function?

[@NicholasJMV1981]

+Monica Jean Busog Basically, if a y-value is not in the range, it won't be surjective and therefore won't be bijective. Think about any quadratic equation. There are tons of y-values that do not exist. Think about x^2. There can be no negative y-values therefore, the function can't be a surjection

[@floatgoat1]

This may be a dumb question. But if you restrict the range for y=x^2 from [0, inf) can this function be considered onto?

[@dannuttle9005]

It's not a dumb question, it's a very good question to ask. As I understand it, the definition of the domain and the range (or more particularly, the codomain) are important in determining injective and surjective. Yes, if you restrict the range for y=x^2 to [0, inf], then it is onto. Wikipeidia says "a surjective function is a function whose image is equal to its codomain." The key word is codomain. It may be the same as the range, or it may be a subset of the range. IF and only IF the codomain is defined as all reals, then y=x^2 is not onto. Would appreciate any correction if I've misstated or overlooked anything.

[@NicholasJMV1981]

Yes you can restrict the domain and it can be an onto function

[@VIVEKKUMARSINGHRAJORA]

really great explanation..

[@NicholasJMV1981]

Thank you!

[@theskeletonful]

The right diagram on 3:48 wouldn't be considered One to one right?