Next Video: th-cam.com/video/2zeYEx4eTdc/w-d-xo.html Final Exams and Video Playlists: www.video-tutor.net/ Functions and Graphs: th-cam.com/video/ZTEv8OnGaxo/w-d-xo.html Transformations of Functions: th-cam.com/video/tyQLp6x-GoU/w-d-xo.html Graphing Polynomial Functions: th-cam.com/video/rOOefdqMvtA/w-d-xo.html
Wow! You make the concepts clear and understandable behind the "madness" of math. I really enjoy watching your videos, esp when I struggle. You help by setting a foundational understanding to functions. Just finished watching your multiplicity video and now I get it. Thank you. I wish you were the video instructor on our Moer portal for math!
All of your videos are so simple and easy. I normally don't comment, but your videos have been so helpful while I prepare to take calculus this semester. Compared to professor's videos and other resources, you just make learning so clear. Thanks for all your videos.
Thanks sir. Your videos are so good. I always grasp the contexts very easily due to your unique way of explaining ideas. Thank you sir. I love you. May allah bless you, amen 🙏
You sir have saved my back and if you are ever in need of help just say something because after watching your videos all hope is not lost and I might just pass math.
The end of this video is a bit confusing I think: f(x)=x^2 is a function. It passes the vertical line test. But it fails the horizontal line test. So it is not a one-to-one function (I had to look this part up elsewhere). The inverse is NOT a function, which he shows. f-1(x)=±√x has two answers, the positive √x and the negative √x, which means it's not a one-to-one function. When you plot both of these on the graph, together they fail the vertical line test. Btw, the horizontal line test is ONLY for the original f(x) function to test if its inverse would be a function. You don't use the horizontal line test after you've already drawn the inverse on the graph. That would just be crazy talk.
simply put, f(x)=x^2 is a function, it's inverse is not a function if f(x) passes the vertical line test it is a function if f(x) passes the horizontal line test it's inverse is a function
He lost me at the very end, BUT to answer your question: Use the vertical line test on f(x) and if it passes, it's a function. But use the horizontal line test on that same f(x) line to determine if the inverse is a function. Once you've drawn the inverse onto the graph, then you go back to using the vertical line test on it. In other words, the horizontal is only used on f(x) to determine the inverse. Do not use the horizontal line test on the actual line drawn from f-1(x).
@@dilawazranidilawazrani5549 Only then that he must tell you or assume that you know that √-x is not a real number and so the functions range does not include √-x and then function piece can be inverted without any problems.
it does not have inverse function as it failed with horizontal line test for y= x^2, but I think we can show what we can get x = y^2, rootover(y^2) = +-rootover(x), y = positive rootover(x), or negative rootover(x).
Great Video!!....however I think you should clarify your language a bit. The inverse OF a function is not the same thing as the inverse function. The inverse of a function need not BE a function while the inverse function must be a function.
hey question about 2:06. I thought that in order to be a function each domain needed to have exactly one corresponding range but putting plus minus gives two domains which confused me
Yes, x square has two solutions. A function must be bijective (one to one and onto type function) function in order to have an inverse function. Hence x squared does not have an inverse function (somewhere near the end of the video he said x >= 0 so that can make sense). Other way to explain is that sqrt x does not exactly inverse the effect of the function because it gives both negative and positive outcomes
i think the first question is wrong. how is 3y-1 multiplied by x equals to 3xy-3x. i understand the 3xy part but how did the 3x happen? there is no 3 to multiply it with ? or maybe i am trippin
1. how to find inverse function 2. how to know if 2 functions are inverse function of each other 3. the property of inverse function 4. how to draw the inverse function 5. how to know f(x) is a function? 6. how to know the inverse is a function
so confusing about how you explain to test the graph using vertical and horizontal line you said used a vertical line for the original function and horizontal line for inverse function ???????
Domain is the values for "x" Range is the values for "y" Its used for arrow and mapping diagrams when you substitute the number into the function Example: (2) --> (y) 4x - 1 = y 2(4) - 1 = y 7 = y Therefore: (2) ---> 『y=4x-1』---> (7)
my temporary math teacher has some anger issues or something, she kept screaming when we dont know the answer but she doesnt know she didnt explain it too well gladly she's not our real teacher
You explain things clearly, but some of your examples are wrong. f(x) = x^2 - 4 is not a 1-1 function, therefore has no inverse. You should have noticed this when you took the square root of y^2 which gives two answers. If you limit the domain of f(x) = x^2 - 4 to [0, infinite) then it has an inverse.
Next Video: th-cam.com/video/2zeYEx4eTdc/w-d-xo.html
Final Exams and Video Playlists: www.video-tutor.net/
Functions and Graphs: th-cam.com/video/ZTEv8OnGaxo/w-d-xo.html
Transformations of Functions: th-cam.com/video/tyQLp6x-GoU/w-d-xo.html
Graphing Polynomial Functions: th-cam.com/video/rOOefdqMvtA/w-d-xo.html
this is the only youtube channel i will watch adds for cause this man deserves it
FR THOUGH😩
What a witch
Hii
i thought add money went to youtube
@@Saylurs youtube takes 45% and creator takes 55%. if youtube took all the money there would be no incentive for a creator to monetize their videos.
I literally studied this for hours just for this man to get me to understand it easily after one example problem
Wow! You make the concepts clear and understandable behind the "madness" of math. I really enjoy watching your videos, esp when I struggle. You help by setting a foundational understanding to functions. Just finished watching your multiplicity video and now I get it. Thank you. I wish you were the video instructor on our Moer portal for math!
Same when I forgot my lesson cuz I didn't take note😎 during online class
ONG
All of your videos are so simple and easy. I normally don't comment, but your videos have been so helpful while I prepare to take calculus this semester. Compared to professor's videos and other resources, you just make learning so clear. Thanks for all your videos.
Beautiful, clear and straight forward class
Who’s studying for their test next period 😅
me!
Right here lolol
Dude this is me right now 🥲
rn
Actually 😅😅
Thanks sir. Your videos are so good. I always grasp the contexts very easily due to your unique way of explaining ideas. Thank you sir. I love you. May allah bless you, amen 🙏
Weird, only 12 hours ago I had math class and this is what the lesson was about.
Yes same time
😂
i wish all the best for you man thank you so much for your great videos!!
I love your videos man!! They are so useful especially when there's an exam. TNX
I love you The Organic Chemistry Tutor.
You sir have saved my back and if you are ever in need of help just say something because after watching your videos all hope is not lost and I might just pass math.
The end of this video is a bit confusing I think:
f(x)=x^2 is a function. It passes the vertical line test. But it fails the horizontal line test. So it is not a one-to-one function (I had to look this part up elsewhere). The inverse is NOT a function, which he shows. f-1(x)=±√x has two answers, the positive √x and the negative √x, which means it's not a one-to-one function. When you plot both of these on the graph, together they fail the vertical line test.
Btw, the horizontal line test is ONLY for the original f(x) function to test if its inverse would be a function. You don't use the horizontal line test after you've already drawn the inverse on the graph. That would just be crazy talk.
simply put, f(x)=x^2 is a function, it's inverse is not a function
if f(x) passes the vertical line test it is a function
if f(x) passes the horizontal line test it's inverse is a function
@@user-eu2mg8lw2t Ha, yes, succinctly put. You should've seen my comment before I rewrote it entirely. I was so confused.
@@user-eu2mg8lw2t agreed
thank you lol needed this, I had it right but the last part just made me second guess it.
MR. Organic Chemistry Tutor, thank you for a solid Introduction to Inverse Functions.
When i hear this voice i know i am about to pass all my exams ❤ "in this lesson" omg lobe him😊
you are my literal savior omg 😭
saved my ass today man. Uni profs r terrible so thank you for being great
I think there is a mistake with x^2 - 4 . You cannot have that since x+4 = y^2 means two answers. y^2 is always equal to two numbers. -/+ sqr(X+4)
Yes thats right
I don't understand. Please elaborate further.
@@B6lpl can you please explain to me what he/she was trying to say? he/she didn't express his/her confusion specifically. That's why i am asking you
Smart one✅💯you are the best sir🙏thank you
THIS MANS VOICE -
Same, I could listen to this dude all day
I am 69 years old and I am watching this just for entertainment
A function that is not one-to-one does not have an inverse. The plus or minus does not cure this problem.
could you please make a playlist for only the function from the introduction to the last topic
Nothing but “GENIUS”
I just confused how does people dislike your videos you are a lifesaver
Finally someone who is able to teach online school
You’re saving my grades
Does anyone know how to make an inverse into an original function if I’ve got some points if x is this and f(x) is this?
I think you just switch x for y (look for the inverse) and solve to get y by itself. It’s the same as solving for the inverse of the inverse.
Basically do what he showed you but with the inverse it’s the same thing
Everything is possible but the only problem is people like are very rare in few,the ones that always help direct with their heart.
Kinda like it ,it really helps
So should we always use the vertical line test for the function and the horizontal for the inverse ?
He lost me at the very end, BUT to answer your question:
Use the vertical line test on f(x) and if it passes, it's a function.
But use the horizontal line test on that same f(x) line to determine if the inverse is a function.
Once you've drawn the inverse onto the graph, then you go back to using the vertical line test on it. In other words, the horizontal is only used on f(x) to determine the inverse. Do not use the horizontal line test on the actual line drawn from f-1(x).
@@EmpyreanLightASMR Nice and clear. Thanks a lot!
2 years later and this has helped me thank you i was very confused!@@EmpyreanLightASMR
@@macOS-kw8vr That's wonderful, great to hear. (I'm now in Calc III class!) Keep it up!
i fucking love u and ur channel, literally best channel ever existed ILY
For the bottom half of the sqrt x would that not turn it into a many-to-one function which you cant do with inverse functions
I should pay this guy my tuition.
bro ur the best wallahi
at 2:04 in the video, why did you use a square root? Is that the inverse operation of an exponent?
Isn't he supposed to do this? Cuz when we sqrt both the sides, we get the value of y which is +/-√x+4
2:00 here its mistake: x = y^2 - 4 => y^2 = x + 4 => y= rootover(x+4) or negative rootover(x+4)
He did the same tho
how can f(x)= x^2 have an inverse?
Right
@@dilawazranidilawazrani5549
Only then that he must tell you or assume that you know that √-x is not a real number and so the functions range does not include √-x and then function piece can be inverted without any problems.
Square root
it does not have inverse function as it failed with horizontal line test for y= x^2, but I think we can show what we can get x = y^2, rootover(y^2) = +-rootover(x), y = positive rootover(x), or negative rootover(x).
6:49 the graph shows that+-✓x can't be a function on its self,
Then is it a function itself when its a inverse function?
Great Video!!....however I think you should clarify your language a bit. The inverse OF a function is not the same thing as the inverse function. The inverse of a function need not BE a function while the inverse function must be a function.
I love u sir 🥰🥰, you are the best
hey question about 2:06. I thought that in order to be a function each domain needed to have exactly one corresponding range but putting plus minus gives two domains which confused me
Yes, x square has two solutions. A function must be bijective (one to one and onto type function) function in order to have an inverse function. Hence x squared does not have an inverse function (somewhere near the end of the video he said x >= 0 so that can make sense). Other way to explain is that sqrt x does not exactly inverse the effect of the function because it gives both negative and positive outcomes
@@anniesina1235Yeah this is too important not to mention
Nice dude, you are god :D
Thank so much!
i think the first question is wrong. how is 3y-1 multiplied by x equals to 3xy-3x. i understand the 3xy part but how did the 3x happen? there is no 3 to multiply it with ? or maybe i am trippin
Thanks ☺️
1. how to find inverse function
2. how to know if 2 functions are inverse function of each other
3. the property of inverse function
4. how to draw the inverse function
5. how to know f(x) is a function?
6. how to know the inverse is a function
How can we cancel 3 by 3 when there is addition??? , that def restricts it.
Love the content!
Your the best
The amount of lives you've saved
so confusing about how you explain to test the graph using vertical and horizontal line you said used a vertical line for the original function and horizontal line for inverse function ???????
straight schlompin vid dude
what a legend
2:04 doesn't that not make it a function then?
G 141
Thank youuuuuuuuuuuuuuuuuu
Whos studying while reading the comments 😂😂😂😂😂
What is domain and range I don't understand it
Domain is the values for "x"
Range is the values for "y"
Its used for arrow and mapping diagrams when you substitute the number into the function
Example:
(2) --> (y)
4x - 1 = y
2(4) - 1 = y
7 = y
Therefore:
(2) ---> 『y=4x-1』---> (7)
tyyy
2:03 shouldn't it be +/- why didn't he add that its a square root
In frst eg wht ws those points (2,7)????
he just gave example inverse function work with point x,y = 2,7 for f(x) but it will become 7,2 for f'(x)
Mistake at 2:02 it should've been plus/minus square root of x+4 but anyways really helpful
He....he did put ±√x+4.... if you waited and watched a whole three more seconds later at 2:05
my temporary math teacher has some anger issues or something, she kept screaming when we dont know the answer but she doesnt know she didnt explain it too well gladly she's not our real teacher
You explain things clearly, but some of your examples are wrong. f(x) = x^2 - 4 is not a 1-1 function, therefore has no inverse. You should have noticed this when you took the square root of y^2 which gives two answers. If you limit the domain of f(x) = x^2 - 4 to [0, infinite) then it has an inverse.
7:07 personal time stamp
Math is everywhere
THANK THE LORDS AHSGAIAHA I HAVE AN EXAME TMR AND IM DYING 😭😭😭😭
Function y =Sinx fails horizontal line test , Does it mean inverse of Sin function doesnt exist , Any one can explain this please.
Ta bien
2nd Question's inverse function is wrong, in fact that function cant have an inverse function, cause its not a one to one function.... PL correct that
You're right brother. You and I noticed it
Man i do not understand this part at all
this man = jesus.
No.
😌
❤
ما فهمت شي
ܳܬܝܓܪܪܝܝܦܟܪܪ ܗܟ̤̤ܺܲܵ ܛܓܪܪ ܢܗ ܗܶܓܐܙܠܦ
@@isaac1674 what language is this
@@Himalayaz Bosniak
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my brain burn out😅😢
Rosalynn Carter died. :(
Hutho
I love this TH-cam channel, but you voice man is very low.🤦♂ do some about it.
yawa
Nothing but “GENIUS”
Nothing but “GENIUS”