How to Find the Inverse of a Function (NancyPi)

MIT grad shows how to find the inverse function of any function, if it exists. The inverse function is the reverse of your original function. It undoes whatever your function did. If your function takes x and gives you y, then the inverse function takes that y and gives you back x. Nancy formerly of MathBFF explains the steps.
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How to find inverse functions: There are three steps to finding the inverse function, if it exists. The first step is to replace the f(x) with just the variable y. Second, swap the x and y variables everywhere they appear in the equation. Third, solve for y again so that you have just "y=" on one side of the equation. If this relation is a function, you can then replace the y with the "f inverse x" notation, or f^-1(x). To know if it is a function, use the Vertical Line Test or consider the form of the equation. Remember that in a function equation, for every x you input into the equation, there can only be one corresponding y value. For an example problem, jump to 00:43 in the video.
For more of my math videos for algebra, algebra 2, precalculus, and more, check out: nancypi.com

[@bert221221]

Good lord, respect.
"Why is this important?"
"Great question, I don't know. But screw it, here's an easy explanation that won't require 30 minutes on Khan academy"
Thank you Nancy, much appreciated!

[@ray-annarodney2952]

Lord*

[@cefb8923]

Two things I love in this comment, one, why are we learning any of this crap? (So it can be a wash out course to make people go take liberal arts or business degrees) Awesome! Why learn things that will be useful in our future careers!
Two, NancyPi > KhanAcademy.

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[@user-mn4zn6jx4j]

I hate khan academy

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Nancy's voice is so soothing it makes me understand the topic in question much more easily.

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Actually has a hint of sarcasm

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This is one of the characteristics of a serial killer (jk)😂

[@raymondwolf_1017]

When you have a test in 10 minutes and still don’t understand anything- thank you!

[@mmaighrd]

Next video: how to reverse letters

[@pips_queaky]

Teaching math with inverse writing? Who the heck can do that? except you. RESPECT. From PH

[@YellinHelenP]

You are so relaxed and clear you are a gift! You take something that induces stress become a calm experience so that learning really begins.

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Me : why do I want to learn this?
Nancy : I don't know your teacher wants you to do this
Lol😁😁😁

[@MG-nb1nd]

Hahaha

[@miaulink1152]

Somehow or another it's used (or gone back to) in calculus with derivatives. I'm in a section on it, but since I can't remember how to do inverse stuff, that's why I'm watching the video.

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Me too 🤣🤣

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[@Niovo]

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!

[@SpeedyWeedyYT]

Nancy is a life saver for people with ADHD. She explains it slowly so we can follow along, and I love her for that.

[@somacruz7758]

I have to say this, I was nervous and full of anxiety just by trying and not getting it. I stepped back and took a break but I told myself I can’t give up. So then I found your video on a whim just by trying something. Man you saved me and now I understand, I’m thankful for this video and your help as well as my teachers. Thanks again!

[@cjpopkes9627]

Always the best explanation and presentation. NancyPi is the first and only resource needed when my kids need some homework help.

[@s_patzz8212]

Watching this during Corona-lockdown... I've been reading a lot of popular physics so far and as it's been going well, so i thought to myself i really must get my head around calculus. Knowing that @NancyPi is the absolute best i figured, start at the very beginning of her precalc series. Having watched this first video, i'm happy to report that I am none the wiser and now there is a nerve twitching on the side of my head :)

[@bilton3183]

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

[@nathanmclaren8361]

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

[@DanieWise]

Your videos are the only helpful math videos I have watched! Thank you soo much!

[@PoeticSonic]

thank you it was very clear with a usable example rather than in other videos. again THANK U

[@vive335]

Helpful, she explained in very easy words. I like teachers like that. I’m not very experienced in math.

[@isaiahmoss2892]

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

[@ed684]

Why you explain so clear..you are saving my life!

[@sayleeraut]

thank you so much for this🥰everything is crystal clear❤

[@geeklafreak2638]

Thank you for all your videos and hard work

[@Sophia-fc9qn]

A true savior. Some one I can actually understand

[@michaelpappas3857]

Excellent explanation! Thorough and concise.

[@muhammdmahedi3070]

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

[@davidschmidt5507]

I don't know if anyone will believe me but I actually used this in practice in my life when I was building stuff so thanks for the refresher video!

[@chamindasilva7629]

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

[@jeramellg1]

Thanks so much for this Ms Nancy 💖

[@KitanaiharE]

Your vids are a godsend.

[@syedamanat6241]

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

[@davidkwon1872]

Thank you. This is so good to my son and daughter.

[@shinchananddoraemonlover6278]

Hi nancy would love to see more video lectures of yours.

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Great videos keep up the good work

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UR VIDEOS ARE THE BEST

[@kuonkhailechdawech2309]

You are the best Nancy!

[@justjacqueline2004]

Great clarity.

[@frs535]

Fantastic explanation!

[@camurgo]

Good video. I had forgotten this stuff.

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

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Peace

[@rlewis1946]

You are a wise person to seek knowledge from a truly gifted teacher. We wish you the very best in your mathematical studies!
RL Buffalo, NY USA

[@tomdugma1]

whats the name of the university?

[@haram7359]

I love u, and u make me love math

[@gyannyyeboah9453]

Thanks a lot, you made it so simple.

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I love your teaching skill

[@lutaayaabdulwahabu7680]

The best teacher, I've got the concept 🤓🤓

[@IlaizaMendoza]

omg thank you i need this kind of exampleee!!!! thank you

[@NJCC2011]

Thank you, NancyPi :D

[@lealdeadonisjason5616]

Thank you so much it help me a lot

[@mistermeaty993]

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

[@kibhab6414]

You are great Nancy

[@kushpatel8199]

i actually needed this ,3

[@davidramrod7610]

Very helpful. Thank you!

[@metalmanny0000]

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

[@con-0310]

very helpful video, thanks:)

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best tutor out there

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I LOVE YOU NANCY

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you're a life saver

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Thank you!

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i am in love with her voice❤️😍❤️

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Thank you very much appreciated😤

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Thankes you for nancypi

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You deserved a subscribe and likeee 🥺💖

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Your the best one nancy

[@thomasdestry5188]

🎉Thank you so much‼️

[@parmindersinghraj7424]

thanks for the video!!!!

[@runforestrun3556]

Why am I watching this at 4 AM. Idk
But I learned something though

[@seahorseanemone5258]

So much better than my maths lecturer.

[@orp0piru]

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

[@dicklexiclemon7487]

LIFE SAVER

[@ALLCAPS]

Thank you!

[@rahmayiga1101]

Thanks 4 your video

[@DavidPaulNewtonScott]

Fabulous as usual save hours of reading.

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thnk you nancy for making such videos
love from Afghanistan💌

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Niceeeee thank you!

[@aryamansarkar]

nice video maam love it

[@FeliciteMnkusi]

Thanks nancy you really help me 😁🇷🇼

[@anismatar]

One comment about swapping x and y I think people do it so they can later on solve for y as they are used to since y actually represents old x but makes the dealing with equation easier.

[@shadrackokello8228]

Sending my love❤❤❤ from Mombasa Kenya 🇰🇪🇰🇪 Nancy 📍

[@danielmayo1336]

I learn math teacher and still make my English more improved. Daniel Mayo Rio de Janeiro, Brazil 🌹💋👏👏👏👏👏👏👏👏👏

[@jensmalzer6344]

Do u have the coronavirus

[@hamsack981]

Make linear algebra vids please. Thanks Nancy!

[@CarlyDayDay]

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

[@user-vp2uo2xh7f]

Thanks Nancy you're real asf

[@Ellen_Moshaga]

i think you the best math teacher ever...

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Yes

[@ckmc05]

Thank you for your videos....from Philipinnes

[@monzirmohamed6878]

Like the vidio helped me with precalculus

[@matthewantrim3472]

Thank you

[@isidorosargyroudis4128]

thaaaank you. Ευχαριστώ κούκλα

[@edwardmulenga7783]

Thank you Nancypi..... I have an exam tomorrow

[@sumayya003]

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??

[@mubaarigkoosaar9150]

Good lesson

[@miaagainsttheworld]

thank you omg

[@preet9343]

so is the inverse in discrete math the same as transpose in linear algebra?

[@benjaminjvredevelt]

Nancy,
Thank you for your positive influence.
Love,
Benjamin

[@PrincessSakuno]

Thank you

[@DeepakJain-tg3il]

Thanks

[@queenanne2367]

Great video! this helped me a lot, doing some review just to be ready for my online classes. I'm a stem student btw hueeeee idk why i chose this. byeee engineering here i go jk

[@noorpamirian8401]

nancy which type of software do you use for writing

[@justrightpath]

this is what i wanted

[@mics.]

wait, let me watch it again, i was too amazed by the way she writes to understand a single thing earlier.

[@Mazharaly]

Amazing

[@jamgamer]

This is way better than my lecture wtf

[@gunnarjensen5910]

If F(x) is a simple multiplication or sum of parts ??

[@imgood2107]

I love you Nancy pi