Hi guys! I’m Nancy and I’m going to show you how to find the inverse of a function. What’s an inverse? An inverse is just the reverse of a function. It basically undoes whatever your function did. So if your function takes X and gives you Y your inverse function is taking that Y and giving you back X. Why would you want to do this? Good question. I don’t know! but your teacher wants you to so let me show you how to find the inverse function. So what you’ll already need to know is how to tell if something is a 1 to 1 function. So for every X value you only have one corresponding Y value. OK. So say you have a function like this f(x)=(x + 2) / x. and you need to find the inverse if it exists. Of course for this function we also need to keep in mind that X cannot equal zero. because we can’t divide by zero. The first step Is just to rewrite f(x) as just Y. So we would just have Y equals (x + 2) / x. Then this is the most important step you need to swap X and Y. So you switch X and Y everywhere they appear. So we would actually have X on the left side instead of Y. Here on the right side replace X with Y everywhere. So we would have (y + 2) / y. Last step you need to solve for Y. so that we’re back to Y equals with Y alone on the left side. To do that we’ll need to clear this fraction. So you would multiply both sides by Y to clear the fraction. and then get in the next line (x * y)=just (y + 2). because we’ve cleared the Y. Then if you want to get Y alone you’ll need to have all your Ys on one side. Why don’t we just bring this Y over to the left by subtracting it from both sides. So you get (x * y) – y=2 Now to solve for Y you only want Y to appear once on the left side. The best way to do that is to factor out a Y. So you’d have y( and what’s left is x – 1=2. Final step Divide out the (x – 1) from both sides. So you have y=2 / (x – 1) To write this as a function we would use inverse notation. finverse (with a -1 superscript) of X equals the expression. But first you have to check this is actually a function. Sometimes it’s just a relation and not a function. Is this a function? It is because for any one X value we plug in there’s only one corresponding Y. And if we look at the graph of this function as you know it would look something like this. So if you did the vertical line test and checked everywhere it only intersects once. So it’s a function. So we can use this notation. f inverse (x)=2 / (x – 1) If you found that it’s not a function you would just answer “inverse function does not exist”. So your answer for the inverse function is f inverse (x)=2 / (x – 1) So this one magically worked out. But some things to look out for where you may not have an inverse function and your inverse function doesn’t exist is if you have a y^2 somewhere here in your equation. Or you have a graph that could look something like this. Where if you drew a vertical line it would cross more than once. Might cross twice. You wouldn’t have a function in that case. So you wouldn’t have an inverse function. and you would just say “the inverse function doesn’t exist”. I hope this video helped you understand how to find the inverse of a function. If it exists. If it did help you please click “like”!

Hey NancyPi! Thank you for making awesome math videos. This one about inverse functions really made sense. Your channel has inspired me to make my own youtube math tutorials to help students. Keep up the great work!

Even though i didnt watch it, i'll hit the like button because Math education support by Nancy is what most students need.

NANCY

I love u, and u make me love math <3

Thank you! <3

Have you ever done a video on the precise definition of a limit?

Hi

I am a university student from the State of Palestine and follow your channel first and take advantage of your explanation.

Good video. I had forgotten this stuff.

I looooove your voice

just when I need this !

i actually needed this ,3

I have two questions. 1 – What if the function is something different than x+2/x? 2 – Couldn't the function have two solutions like the quadratic equation?

Great videos keep up the good work

I love you Nancy

what invert would click thumbs down

Great clarity.

Y

Hey can you plz make a video on alevel math trigonometry

Can you plz wear more makeup in your videos. Not that you aren't pretty it's just that it's nice to have some eye candy you know

Thank you for your videos!!! Its really helping me, I am a part time engineering student.. This really helps me understand maths much better

Make linear algebra vids please. Thanks Nancy!

Thank you <3

Hey Nancy please make a binary operations tutorial video please

When a function isn't one, when there are multiple y values for one x value, then why is sqrt(x) even a function? For x=4 I've got y=2; -2.

I wanna suck your toes

Thank you so much. I am good at math but been out of school for a while. Your explanation excellent.

Thanks for teaching me how to find the inverse function of any function.

Thanks for the video. One example of why we would need inverse functions is security. There are two way to hide what you wrote, one is using an encryption function and another is using an hashing function.

Encryption functions have inverses, so a cryptic mail sent by you can be decrypted using a decryption function. This decryption function is the inverse of the encryption function used by the original sender.

Hashing functions on the other hand, have no inverse functions and therefore more secure. The thing is, receiver of the mail can't decrypt your mail so it doesn't make sense to use it in that context. One useful area it is used is password databases. For example, when you sign up for Youtube, your password will be hashed. So "hunter2", your password will result in a text like "6y3478twed" etc. Now, when an attacker gets the database, s/he has no way to access your account. Because if attacker were to type "6y3478twed", it will be hashed again and when compared to hashed password in the database, it will be different. Since there is no inverse function, attacker can't get the original text neither.

There is only one way to access your account then. If, as an attacker I have hashed versions of the common passwords, I can search for the passwords I know in the database. So, use uncommon passwords.

Ur a smokeshow

Can you do integration by parts cal 2? Just covered this yesterday and definitely could use a video over that please 😃.

How does the original function's limitation (x cannot equal zero) limit the usage of the inverse function?

how do you know what direction the lines are going on the graph ?

omg thank you for starting off with explaining what inverse of a function actually means. Had a hard time understanding what it meant. Great video!

Why is it x-1 instead of just x?

A true savior. Some one I can actually understand

Still confused though..

1 a.m. and i have been studying for my final since 10 a.m when i woke up thanks for the help

Must have took a long time to learn how to write backwards.

thnk you nancy for making such videos

love from Afghanistan💌

فديتج جنننننننن شرحهااااااا

😍😘😘😘😘😘😘😘😘😘😘😘

Make a video on differential equations

How do you make the inverse function come back to normal with no ^-1

thank you omg

it's difficult for me

I just watch her teach cause she's hot and smart

You are my best teacher . U make math easier. Thanks a lot

You write everything opposite right?

Thank you for all your videos and hard work

Why the hell do you talk so slow

How did you get y(x-1) from xy-y?

thanks for the video!!!!

1000th like lol

Good lesson

I understand how to do it, I just don't understand what the point of this function is. And how do we consider y=f(x) but then it's also y=f^-1(x), y should be y=y, but it's also two opposite functions??

THank so much Nancy. You have opened my future in this topic and where you explained about domains. .

Thank you, NancyPi 😀

💆♀️ me no understand; too much changes

why isnt anyone talking about how beautiful this gal is!

Your vids are a godsend.

Demonstrated with inverse writing. Respect.

If she was my maths teacher I won't skip a single class😚

i think you the best math teacher ever…

I ate a potato before watching this video.

Can’t concentrate

I love you

This video really helped,but i really wish she would go over graphs more. Otherwise shes amazing.

How can you do that??

Writing backwards

Next video: how to reverse letters

what grade is this for?

i took PRE-Calc in high school and had a very BAD attitude about it…I thought they should have been teaching Calculus in High school. my friend in Florida was taking calculus at his high school , thus i thought this class was like a place holder , a nothing class because the school teacher could not teach calculus because he was too dumb or something .. i felt like i was in a remedial class… BUT THE FACT IS….. this class forms the basis for A LOT OF CALCULUS and when you factor out calculus equations , you have to know the steps you learn in PRE CLAC…I just wish my teacher would have told me this .. thus I want everyone who is learning this , learn this as well as you are able , it will make Calculus a breeze …. I took two years of Calculus and I was always thank full for my GREAT math teachers in high school..

Thanks!!! ::::::::::::::))))))))))))

Thank you so much it help me a lot

So cute

Thanks…

Is this the range of a function

Like this comment if you’re here for mr.gaugler’s class

According to Nancy….why do we want to do this? "I don't know!" This is a very disappointing answer from a very good teacher.

Is this on SAT?

no more vid?