Inverse Functions - The Basics!

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Inverse Trigonometric Functions • Inverse Trigonometric ...
All of the fundamental ideas of inverse functions are discussed. What exactly is an inverse function conceptually? Which functions have inverses? How do I graph inverse functions? What are the other basic relationships?
I do not actually show how to find an inverse (I thought the video was getting too long!). I also already have videos about how to find inverses, so I will provide a link somewhere!

[@Lexyvil]

You have taught me more in 17 minutes than my professor did in a whole week. Thank you very much!

[@AceofDlamonds]

Lexyvil Can I teach you spelling for 17 minutes too?

[@Lexyvil]

V Ling Oh, haha, my bad I found my mistake ^ ^ I put thought instead of taught ~ Thanks. These two words are similar *Edits*

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+Lexyvil if you speed it up its even quicker!

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[@patrickjmt]

@narkatika unless the domain was restricted in the original problem and you forgot to mention it, it is not 1-1 and has no inverse. i think this is one of the very first things i mention in the video. t^2 would be a parabola and hence fail the vertical line test.

[@muhammadmadyun3790]

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[@ademBizon]

That's really awesome explanation After 10 years and people still learning from your videos Thanks a lot

[@patrickjmt]

@Magezxzx did you even search for it? there are a bunch of videos on it already by me.

[@taalpgh]

Thank you! I have such a hard time in my calculus class because my professor cannot explain simple things....AT ALL. And thank you! I finally get it!

[@bhimgrg05]

Thank you Patrick. You explained it better then my professor. Thanks a lot. Keep up the good work. Thanks again.

[@patrickjmt]

@narkatika it does not have an inverse as it does not pass the horizontal line test (not 1 to 1)

[@gretaoakley9666]

Everytime I have any quires about maths, i always turn to you. Thankyou for breaking it down and explaining it in a way which makes sense. Im studying to be a high school maths and science teacher and your videos demonstrate the teacher i want to be. Thankyou!

[@patrickjmt]

glad you like the videos :) i had more than a few teachers like that myself...

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This is the first video i saw on your channel. And you explained the basics so well that i wish my teacher knew how to teach this topic like you did. You are my new online teacher for sure! Thanks a lot.

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I've had so many people try to teach me this concept but I never got it until I watched this video....one video did what so many people could not...the reason being is because you explained why, how, how to check, and why again. Thanks so much for your help! You're a saint! (a mathematical saint)

[@sail2byzantium]

Very nice. Esp. liked the beginning with the 8 to 3 and 3 to 8, etc. examples to show the inverses. Excellently explained. Thank you!

[@patrickjmt]

@Vorbis5 i am flattered that you find my videos enlightening

[@nanokd]

Patrick you make math seem fun! I love watching ur videos, they r extremely helpful.thank you 4 sharing your knowledge :)

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Your teaching method is awesome Patrick. Great job! Love the video.

[@patrickjmt]

@MyMastewal1 what do you mean, ' whoever made it ' - it clearly says i made it! : )

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[@kibethnehema2069]

This makes so much more sense than my text book which just defined what a function is over and over and said that an in verse function is notated by f^-1 then expects us to work problems...

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If you are not a math teacher, then you must become one. You MUST become one. It is your duty to share your amazing gift for teaching math to all the poor students with incompetent math books out there.

[@patrickjmt]

@baburo101 almost done with the calculus playlists, will get to algebra next

[@patrickjmt]

@nanokd glad you like my vids : )

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Awesome Patrick. Got lot of clarity

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Daamn you deserve some credit for the teaching skills you have got. Very helpful sir ;)

[@patrickjmt]

@MrAMorris7 happy to help : ) good luck in your solo studies!

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Thank you for this. I made a 56 on a quiz, so I watched this while I was studying. This made the test so much easier you have no clue. Thank you again, and I hope you like your new sub.

[@TheBobstar89]

Thanks heaps Patrick! I was following lecture notes on inverse functions but I could never grasp it, probably because I'm more of a visual learner than a text-based learner, so you going step by step through it really helped :D

[@whatheheack1]

I hope your videos go all the way up to calc 4 because this helped a lot!

[@phoenixwings6441]

I like how you said that you start with a number and the other equation gives the number back. It makes sense now !

[@MyMastewal1]

this video really helped me out, whoever made it makes me like math more. thank you man.

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Hi Pat, you do a very good job!

[@0591CAndy]

just finished the video, you explained very well. Thank you so much~! will keep watching your videos~

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I did not understand my teacher nor my textbook and I spent hours reading and in class and I click on your video and in 17 minutes I'm a genius

[@1beautymark]

Thank u so much for your videos. They are saving my life in PreCalc!!!

[@Seattle206723]

Thanks man for the videos, i'm going to look to see now if you have graphing inverse functions.

[@johnterrell3703]

The Big Idea introduction was perfect!

[@jriver64]

If only my teacher could explain it as you do, making it so easy to understand. Thank you.

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[@madknacker]

I'm not sure if it was pointed out, but at 9:21 you stated that because it failed the HLT that it is not a function. I'm sure you're aware that it is still a function, it just doesn't have an inverse. It may be confusing to some. Otherwise great video!

[@messedupworld2000]

Ethan Knack I believe that he meant not one-to-one function, not "not a function", and yes it is still a function.

[@VirtualCurry]

Ethan Knack Thanks for pointing that out! I was reading a calc textbook and it said that a function can have two or more independent variables mapping to a single dependent variable (failing the horizontal line test), but a function cannot have a single independent variable with more than one output or dependent value, then that would be failing the vertical line test. Does that sound right?

[@alfia6690]

+Ethan Knack Important point! Explaining a one-to-one vs. a regular function might have been less confusing.

[@valentinanongthombam3810]

Ethan Knack yahhh as we know there is many one function which pass HLT...still a function I was also thinking U have already watched 2 years before and I am watching only now lol haha

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Thank you! Your explanations are great

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[@patrickjmt]

happy to help :)

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that was a PERFECT explanation !! thank you so much

[@ngkitmayvannessa894]

Good job! Gave me a good understanding on inverse functions.

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[@patrickjmt]

@PrataManiac no; f ( f -1(x)) = x

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[@patrickjmt]

@x3Heroiinex3 thanks : )

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[@Pater_Robert]

Yes, I believe so. I'm also new to this but I'm pretty sure. Because you swap the X and Y coördinates, you'll get a mirror-image to the line x=y. In other words. If you calculate the length a line from any point on the function that is perpendicular to x=y, to x=y. And you'll draw that same distance perpendicular to x=y on the other side of x=y, you'll reach a coördinate of the inverse. e.g. : draw a line from (1,0) to x=y (0,5;0,5), (length sqrt 2), continue, and you'll reach (0,1). GL&HF

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hey patrick could you do a tutorial on graphing logarithmic, natural log and exponential functions (along with their transformations)?? Please, this topic always confuses me just as much as the sine and cosine ones. But after I watched your video on sines and cosines, things made a lot more sense to me..

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