Introduction to function inverses | Functions and their graphs | Algebra II | Khan Academy
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- čas přidán 15. 07. 2010
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Introduction to Function Inverses
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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why cant my schools just play your vids in classes???
Lol, your comment is four years old. Just simply take online class, and when you're in a bind, look for a CZcams video. I just like to learn the basics first by finding the solutions to get from Point A to Point B of the problem. That is all I really need to know. Why do teachers need to spend 30 minute to an hour on a specific type of problem? I feel like the problem is you gotta try and explain it in different ways to 30 students in one class when you could just watch this by yourself and have no problem solving it and actually seeing it visually.
Oh how the time changes, watching this is my math class and I am in public school, a pandemic really changes things.
@@supercoolmunkee but not all has internet connection bro
@@jasinsworld3095 But nothing's fair. Some people just have to work harder than others to get to the same level.
Becoz schooooools want us to become fool by paying some of our lovely moneyssss
its just amazing how this video is uploaded way back in 2010 but is still very useful today and will be for the years to come. Thank you Khan Academy!!
tbh, cant even remember using social media before corona 🙂
Teachers in our school just complicate it as much as possible to mash our brains...but you Khan Academy are something that brought help to me and many other people...I am making progress in math only because of you and not because of my teachers...they are very bad,thank you,keep going.
When you realize that all of years spent in elementary and high school are useless it's such a shame. Teachers only teached us how to calculate something and telling us to remeber all that formulas. They never teached us concepts and we have never had motivation to learn.
I wouldn't say all teachers, but I do feel like there are some who don't teach it that well.
@@benjaming4659 Dear Benjamin, they are very competent, but the way they teach us is not the right way. But it's just the way it is. You will learn the process of solving examples but the idea, history, goals, real world applications you just need to learn by youself. If they know all that yet why they don't tell us?
Don’t know about your teacher but my techers tech almost in the same way as Khan Academy, I just need more time to understand. So, I can watch this video whole day (whereas I can't ask my techer to explain me the whole day...) Teachers really do there best. :)
Thanks Khan Academy. 🙂
Nice watching this 10 years later cause of corona🦠
Same
same
Oml same😂
hehehehehehehehehehahahahahahahahahahahaha
same!
THANK YOU KAHN ACADEMY YOURE MY HERO IF I GAVE YOU A DOLLAR FOR EVERY TIME YOU HAVE MADE EVERYTHING CLEAR I WOULD BE IN REALLY BAD DEBT
LOLOL
fatherless
@@fatcow6636 that's you
@@fatcow6636 You are the one that's acting mad fatherless here.
@@fatcow6636Says the person named 'Fatcow'
5:15 Additional notes from me: a variable is a "bucket" that can be any number based on its constraints and can be changed to any symbol, letter, or maybe shapes (it's basically anything distinct to be used to represent the "bucket") without changing the value of the expression.
Up until x = f inverse of y = (1/2)y - 2, y is useful to see where it's coming from: it's coming from the original equation y = f(x) = 2x + 4, we just solve for x in terms of y to map from the range back to the domain or to make the output as the input and vice versa (that is why it is called inverse function).
After we know where it's coming from, it's useful that at this point and onward, we change the symbol/variable from y to x to see the relationship between f inverse of y to f(x) or f of x. We can do that because we just change the symbol or the variable without changing the value. We could've change the y into a or b or anything, but we chose to change the y into x because we need to see the relationship between the f inverse of y and the f(x) or f of x.
• x = f inverse of y = (1/2)y - 2 --------> change the letter y to X to see the correlation between this equation to f(x) (it's not going to change the value, it's the same as if you were to use star shapes to represent a variable and decide to change them to heart shapes)
• x = f inverse of X = (1/2)X -2
We now see the correlation between f inverse of X and f(x) or f of x. In fact, f inverse of X is derived from f(x).
Notice that it might be a little confusing since now, in the x or f inverse of X equation, the domain (input) and range (output) are represented by the same variable, they are just differentiated by means of capital letter and lowercase letter: x = f inverse of X (let us use capital X as the input and the lowercase x as the output to differentiate them) = (1/2)X - 2.
• The x (range or output) = f inverse of X (domain or input) is similar to the y (range or output) in y (range or output) = f(x) or f of x (domain or input).
• The X (domain or input) in x (range or output) = f inverse of X (domain or input) is similar to the x (domain or input) in y (range or output) = f(x) or f of x (domain or input).
imagine if he taught a class on teaching, then maybe education in America would get better...
Got nothing but praise for this guy. He actually makes sense teaching math.
@chizzy555 Maybe some trades. I could imagine the inverse trig functions would be pretty useful if you're building something.
This video was super helpful. Your ability to explain things makes it unbelievably easy to comprehend and conceptualize these otherwise confusing concepts. It's bizarre that I could spend about an hour in a class with an instructor going over this material and still left not knowing much more than I did at the beginning of that hour, yet I watch this video that's less than 10 minutes, and I totally get it now. However, what I can't wrap my brain around is how 69 individuals found this video unhelpful and gave it a thumbs down.
khan academy is an Easy Mode feature for high school and college math lol
you explain better than my math teacher ever could in his life! THANK YOU! My head does not swim in confusion anymore thanks to your detailed lessons!
THANKS SO MUCH I ALWAYS COME TO YALL WHEN I NEED MATH HELP YOU'RE THE BEST!!!!
I see you've updated your sketch pad. Never thought these videos could get any better than they already were. Thanks, Sal, your a lifesaver.
Dude, like literally YOU'RE THE BEST. Your videos are so intuitive. I love it, I have been after teachers to tell me what's inverse they would tell me it's opposite of what it does, I knew what they wanna say but i felt unsatisfied like it didn't make sense although I knew how to do it. But that part where you just told that question is there any way to get back to the x. After that why you solved for x made perfect sense....
I'm working on a chapter in calculus for about 30-60min + listening to my professors lectures, before I start understanding it well. Then I watch a 9 min video from you and I understand it perfectly... Thanks alot!
Jussst when I thought I had almost all of the basic algebra down. I'm halfway through differential calculus and realized I needed to re learn this :)
Crazy how this video was made before I turned 5 and now I'm watching it as a freshman in college
i would never have made it through half of last year without these videos. thanks so much man.
i had a moment when i had to pause the video just to be like "ohhhhhhhhh" cuz I finally understood. learning over zoom has been terrible but this was so helpful
coming here when my teacher fails (that means i'm always here)
lol
loving the new writing Sal. Much neater!
Woaw man!! Just woaw!! I'm studying Biomedicine at my university, and my professors have tried to teach this to us for a while now, nobody gets it. Then i watched your movie and you explained it sooooo easily in just 9 minutes. THANK YOU!
Hey man how's that biomed going? 7 years flew past huh
Simplifying things so much.has been a great help to understand concept easily.thnk u
czcams.com/video/1NvxOcbb_NY/video.html
Makes perfect sense. Before, I didn't know what solving for the equation did. Now, thanks to Sal, I do!
i love this guy's video, explained much better than my school teacher
Good job, I completely understood but unfortunately not what I’m looking for.
Thank you so so much! Deeply love your channel!
OMG this explain everything! Thanks a lot!
@chizzy555 Would be Algebra II or pre-calc
thank u so much for clearing my concept..
Thank you so much. Your videos are so helpful.
شكرا جزيلا على هذا الشرح المبسط والمفهوم.
sal,u are great..!
made a you tube account just to thank you..!
This part confused me a bit : F-1(y) =(1/2 )y -2 but replacing it with 'x' made me think of substituting y with (2x+4). So F-1 (x)= x
It's a good job he said you could replace it with any other input variable name like 'a' or 'b' otherwise I'd be lost.
Thanks my teacher literally did 2 problems the whole period
I wish you'd actually write out the subtracting and dividing on both sides of the equation instead of just jumping to the answer. It makes it hard to follow along.
And i would like to say i love khan academy
SO MUCH HELPFUL, THANK YOUU!!
Crystal clear explanation
Thank you Khan Academy that you exist!
one perhaps dumb question but I'd like to ask if the inverse of a function really is changing the dependent variable to the independent
I mean if you have say
y = 2x + 1
x = 1/2y - 1/2
if you graph the f(x) you get the same as if you graph the f(y), it is only when you change the y to x and x to y in the second function (the inverse) that you get the correct graph.
Does it only become the inverse function when the switching of the y and x is done? I mean if you solve for x with respect to y you will still obviously get the same graph.
Thanks!
ya; another way of solving to find inverse functions is to switch x and y in the start and solve from there
I AGREEE WE NEED MORE KHAN IIN CLASSES!!!!!!!!
My god, this is amazing.
There are huge problems with the public school system as well as universities.
East or west Khan academy is the best 🙏🙏🙏🙏
Great explanation!!!
Though I slightly understand your point in representing it in graph Sal, It made it more confusing.. (for me) why would you bother to represent it when you already had the f^-1=1/2y-2? Anyway, thank you very much I'll just delve in to the topic of inverse functions to see why did you represent that.
You're the best!
If only all my teachers were this good...
Don’t know about your teacher but my techers tech almost in the same way as Khan Academy, I just need more time to understand. So, I can watch this video whole day (whereas I can't ask my techer to explain me the whole day...) Teachers really do there best. :)
Thanks Khan Academy. 🙂
that just blew my mind
thankyou so much!
Best explanation ever thank you so much
But why do we want to find an inverse?
this is so simple! i have no idea why my sir is complicating it by interchanging the values XD
Hii
Very helpful
I learned this in my algebra 2 class if that helps.
thank you very much
Interesting!
Thank you!!
amazing explanation!!!!!!!!!!!!!!!!!
Here in 2023 😅 this 9m video has been more useful than an hour of my teacher explaining
It's funny how after 2 weeks of garbage from my teachers mouth I was lost and learned nothing but after 9 minutes I understand the whole thing
In 5:58 you say that you can go back to the domain from the range "If possible". Is there an instance in which it is not possible?
Bastiaan . Yes. A quadratic, like f(x)=x^2, will not always tell us exactly where to go back. Ex: f(-1)=1 and f(1)=1. If we go to 1 and ask what value we go back to, we can't say for sure. It's either 1 or -1. Inverse functions always tell us what value to go back to.
Which app you use to record screen?
amazing thank u
at 6:50 did you go the wrong way for 2x shouldn't go to the right and not the left? cause left is -2x
czcams.com/video/1NvxOcbb_NY/video.html
I understood it until 3:59, completely lost now.
+William Stone what do you not understand
6:19 i dont understand why 2x + 4 is plotted on the negative side of x not the positive.
I wish to know how the graph got plotted in that way 😢
3rd comment in a row on one of your videos. Found my new math tutor 😂
Sir please tell me that what is the condition to be the function is invertable
czcams.com/video/1NvxOcbb_NY/video.html
Save my life! Thanks!
Sir ham x and y ko swap kyu krte h
Why do the functions are reflecting over the line y=x?
what software are they using? :3
4:28 u lost me there 😭
I'm a seventh grader being forced to watch this help me but it's kinda cool
SAMEEEE i think its interesting
DanD Fish I'm in 11th grade 😂
@@young9869 sem
YOU'RE MY G BRO UR CARRYING ME THROUGH SAT MATHS 2 . SEND ME UR PAYPAL IF I BECOME RICH THANKS TO U IM SENDING U SO MUCH CASH BRO
I'll give you my PayPal incase you can't get his if you want.
Me 2
Do we need this in life lmao. 😂😂😂
Functions describe situations where one quantity determines another. .... if you don't understand that 🤔🤔 good luck winning the lottery.
It's used in encryption and decryption where encryption is a function and decryption is inverse of the function.
Hash passwords don't have inverses therefore not possible to decrypt
can i ask you why we switch places in the end? pls someone help me. Idk why we switch places.
czcams.com/video/1NvxOcbb_NY/video.html
my math teacher, why didn't you tell me this. My life would have been so much easier.
I turned 17 today
..........chirp..........chirp........
Mariomaniac88 crickets don't chirp and why are you hating on everyone 😂
You're 22 now wow
Ha ha ha
Good 22 now
Bro I hate my math teacher 😐 she is giving us a final on everything we did in 6 months for online school while another teacher left their class a ch test as a final 😐 now I’m stuck here watching all this dudes vids for the past 5 days reviewing 😭
Not all heroes wear capes
how is y/2 the same as 1/2y?
Y/2 means "half of Y" 1/2 means "one half Y". Essentially the same thing.
is f(n) the same as f(x)? thanks to anyone who answers!
mcvdigital yes
what that range figure looks like😁
how do i make an essay about an inverse function : (((
Why no memes here
3:42 This is all I want to know
How did you get half 1/2
thanksss
Voice problem
Why are we swapping the Y in f^-1(Y) with X
Can someone please explain to me why an inverse function is always =y
160000 views and only 250 likes?
Who the heck actually likes this?
Mariomaniac88 people who need help with maths?
راقي
It was a really awesome video but to be honest i still don't understand😭😭😢😢😵
It happens... Keep going 🙂
simple af
*Here 10 years later cause online classes werent fruitful at all*
😑