Domain, Codomain, and Range (Correction)

[@muhammadqasim7143]

Very well explained. The idea of explaining codomain using Venn diagram and the use of Quadratic function made it crystal clear to understand the difference between codomain and range. Thank you !

[@hbsgamer2877]

I agree it cleared a lot of confusion I had and it’s very clear

[@faizanali8799]

Best most talented teacher of math

[@Troglodyte2021]

what's the use of codomain after we know the range already? What is the motivation for this concept?

[@puruagarwal05]

i have this same question

[@tc_iraklis8508]

To be able to tell if the function is onto or not ( f is onto if for every y in the co domain there is an x in the domain such that y=f(x) )... Tbh , I don't find a reason for codomain's existence 😁

[@alanp741]

But....what's the point of the co-domain? I get that it's basically the possible output of the function but all of the examples you've shown all have the co-domain of ℝ. Are there times when the co-domain isn't just ℝ?

[@wiggasknow8261]

How is the codomain of x^2 all real numbers if codomain concerns output? How can x^2 give anything less than zero????

[@josephameh882]

For f(x) = x^2, what happens to when x=0 so the range is not just positive real numbers but including 0

[@HeadphoneTarnish]

First off, given the definitions given in this video, it seems to me that the range can be defined as the minimal codomain- that is, Range = min({A such that A contains the set {f(x) : x is in X}}). Given this understanding, the codomain is a set that includes the range as a subset and possibly additional points that the domain is not mapped to under the function. What interest is the codomain to us then? Is it simply to tell us what kind of set we are mapping into (e.g. the real plane versus the integers), or does it give us some other information about the function? Thanks for the video!

[@centerofmath]

Hello! Thank you for watching and commenting on this video. The range is a subset of the codomain. It is dependent on the domain, what values go in the function, and the function itself. The codomain describes all values that could result from the function which is why there are often additional points that do not overlap with the range. This is because the given domain values do not always cover the entirety of what the function is capable of outputting, but the range is only concerned with those domain inputs. As for your question with the codomain, both statements are correct, and the codomain is important. The codomain is a part of the function and it is something that we are free to define as long as it is within reason. For the example of f(x) = x^2, saying the codomain is all real numbers is correct even though the range is positive real numbers. The range is a subset of the codomain and is therefore valid. In addition, defining the codomain (and domain) can change a question, so it is important to consider it. The function f(x) = 2x on the domain and codomain of real numbers is very different from f(x) = 2x on domain and codomain of integers. There are also cases where limiting the codomain allows for a function to be considered a function. The radical symbol does this; the codomain is limited to positive real numbers and zero. That is why you only get one, positive value of f(x) for each x value for f(x) = sqrt(x) even though both 4^2 and (-4)^2 both equal 16. Hope that helped. Let us know if you have any further questions!

[@nahimafing]

@@centerofmath I don't really understand codomain, you say its all possible output values but if the function f(x) = x^2 then all output values must be positive so how come you said negatives are included (your defininton of codomain was all possible results of the function with any domain) but anything squared is positive

[@benjamingiosis4880]

just explain the co domain please!

[@Hazellites]

Cleared up years of confusion. Hahahaha thanks.

[@PrincessSakuno]

OHMYOGD THANK YOU!!!!!!!!! SUCH A GREAT EXPLANATION

[@agustinbalmaceda3379]

I like how she looks like is speedrunning the lecture.

[@pretty_ok]

Are functions like f(x)=2x or f(x)=x^2 limited to Real numbers for convenience? Isn't it possible to use complex numbers as x?

[@centerofmath]

Hello William Torkington, It is possible to use complex numbers for x, real numbers were used just as an example.

[@maxwellspiano3580]

I would appreciate it very much if you answer this question: a codomain is the possible outcomes and the range is all the outcomes when the input is a natural number?

[@shinYa_ch]

afaik not just N numbers, could be R numbers

[@atikmahbubtanjim4279]

Why only normal number become the domen of 3rd example

[@shlovaski8393]

last example should be from 3 to positive infinity

[@princesahu8186]

That's why I disliked the video

[@allanhenriques2694]

I feel like the easiest way to differentiate range and codomain would be to say, -codomain is where all elements x in A map to some element(s) f(x) in B, -whereas for a range, each element x in B maps to element(s) in A, and each element in A maps to some element in B

[@angelopedralvez6388]

The range is a subset of codomain with the same given function😊

[@nishakarandikar8443]

In second example range includes not only positive real numbers but also zero.

[@centerofmath]

Thank you for commenting on this video. You are correct! Apologies for the mistake. An annotation has been added to fix this.

[@israrullah7727]

Nice way of instruction

[@mlfacts7973]

thanks a lot for your explanation

[@botswanastan7384]

Isn't the domain of x^2+3 minus infinity to positive infinity????

[@toby2237]

It can be, but in this example it was defined as only positive wholes numbers including 0

[@TheXxSPANKERxX]

I FINALLY GET IT!!!!!!!!!!!!!!!!!

[@thedeathofbirth0763]

Wow! This person doesn't even know the difference between natural numbers and whole numbers! And she teaches in a college! Mathematics is about precision!

[@universalponcho]

This was dope.

[@suchandraac]

Will the domain and the co-domain always be equal?

[@centerofmath]

Hi FallingOutWithBoys AtTheDisco, The domain and co-domain will not always be equal. Consider f(x) = x^0.5. The domain for the function can be defined to be only non-negative reals, while we can have the codomain be all reals.

[@suchandraac]

Worldwide Center of Mathematics And for that, range will be defined to be non-negetive reals? Thanks for replying :) Great video btw! Keep up the great work.

[@centerofmath]

Yup! The range will be non-negative reals.

[@suchandraac]

Worldwide Center of Mathematics Thanks again! The video was very helpful!

[@yasir.3486]

That means codomain can have all negative and positive real values? if so then could you please give me an example of a negative codomain value from the above function?

[@emilywong4601]

Who is the lecturer and where is she from? What level are this lecture?

[@centerofmath]

Hello, and thank you for your comment! The lecturer in this video is Chloe, a undergraduate student at Northeastern University. This lecture is at the level of a high school pre-Calculus or Algebra II course, or possibly a College Algebra course.

[@mathguy4264]

Thank you.

[@adarshsinghrathour8594]

Thanks....

[@cocoarecords]

very clear thanks actually

[@user-zp9pp1gt5w]

8:00 where is zero everytime i listen to an american i end up being disappointed

[@benjamingiosis4880]

lol shes out of breathe

[@soumyadreams5598]

u r that beautiful btw thxx 😘😘

[@joyagarwal]

Okay. But I think you should work upon your handwriting!

[@Julia-by6vz]

too much talking. you're explaining everything too fast and its hard to follow. nexttttttt.

[@abhayy2297]

watch it on .75 speed duh.

[@PUMA4LIFE101]

you just stupid

[@ravindrana3606]

Range should be taught before codomain

[@endogatechemistrybyshambhu5944]

No

[@ndukagodstime3012]

I some how agree to this though

[@tc_iraklis8508]

By the definition of a function codomain comes first. If the definition was different we could have avoided the codomain existence.