How to determine if a function graph has an inverse and if the inverse is a function

👉 Learn how to find the inverse of a function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of a function is that when the inverse of a function is made the argument (input) of a function, the result is x.
Given the graph of a function, we will want to determine first whether the given graph is the graph of a function, this we can achieve using the vertical line test. If a vertical line drawn at any point on the graph intersects the graph at exactly one point, then the graph is the graph of a function.
Next, we check if the given graph has an inverse, this we can achieve using the horizontal line test. If a horizontal line drawn at any point on the graph intersects the graph at exactly one point, then the graph has an inverse. To find the inverse of the function, we reflect the graph of the function across the line y = x.
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Organized Videos:
✅ Find the Inverse of a Function
• Find the Inverse of a ...
✅ Find the Inverse of a Function | Linear
• Find the Inverse of a ...
✅ Find the Inverse of a Function | Rational
• Find the Inverse of a ...
✅ Find the Inverse of a Function | Cubic
• Find the Inverse of a ...
✅ Find the Inverse of a Function | Quadratic
• Find the Inverse of a ...
✅ Find the Inverse of a Function | Cube Root
• Find the Inverse of a ...
✅ Find the Inverse of a Function | Square Root
• Find the Inverse of a ...
✅ Find the Inverse of a Function | Table
• Find the Inverse of a ...
✅ Find the Inverse of a Function | Graph
• Find the Inverse of a ...
✅ How to Prove Two Functions are Inverses
• How to Prove Two Funct...
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[@allieramirez162]

Mr. Sir I am in college and my college professor was trying to teach this to the whole class and we were all confused …. when you explained it, it was so much easier to understand … you have helped me since I was in high school and i just wanted to say … you are literally the best !

[@greaserboy4614]

You honestly have a unique gift, and that is explaining and teaching. Thank you for the time and hard work your put into every single video. I, among others, appreciate it.

[@Hanulwalker]

This is so help full, I learn thing here in 10 minutes, thing my teacher takes at-least a full hour of class to teach.

[@brianmclogan]

happy to be able to help David

[@laytonandre2005]

Instablaster...

[@randomthoughts6875]

You're such a life saver🥺 you teach better than thousands of teacher

[@TheHonchoofAllSpearheads]

6:13 because as mentioned previously, the horizontal line intersects the original function's graph at two points, hence the function is many-to-one relation = No Inverse Fn.

[@ilovereadingwuxiaxianxiaat8994]

*wow!*, my teacher took the whole period teaching me this in a way 10x harder to understand. But after this video, I understand so much better :). Thanks!

[@hanifrafli4736]

1:49 very satisfying sounds of whiteboard markers

[@aligu7]

Videos from 2015 are very helpful, thanks for effort !

[@starinsky2873]

Brian you explained better than khan academy lol😂😂😂 cause you combined all the steps i learn then it made clear for me to understand

[@brianmclogan]

happy to be able to help you out William

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[@brianmclogan]

awesome! happy to help you out!

[@annavisagar]

Im so slow in math and i repeat and pause but i understand well, thank you, i like the way you explain it , 🙏

[@brianmclogan]

You are very welcome!!

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[@Iddy267]

how do you do this algebraicly tho? Sometimes you dont have a way to graph it, or at least not in a fast manner of time.

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Brilliant math teacher, I think he's the best on the Internet

[@brianmclogan]

Thanks

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Hey Brian, Thanks so much I've watched 10 of your videos. Online learning is much easier with your videos thank you.

[@jennyke8080]

Please help the following: Find the inverse of f(x)=1-|2ln(x-1)|, restrict if necessary. There is no inverse function for this one since there are 2 roots if f(x)=0 Is it right? Please help. How to do with piecewise function?

[@cjsimon2356]

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[@FunFactopias-Facts]

Thank you so much!

[@sidneyremshik]

good luck on your test tomorrow!

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[@JamesBrodski]

Amazing video. You explained it beautifully.

[@stefankljaic2884]

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[@taonamvududu6494]

Thank you sir

[@مامۆستامحمدبیرکاری]

hi.y=x^2 is not one to one you can finde inverse or not

[@neelpatel5703]

Very helpful thank you

[@fvckinrad6882]

This saved me so much, thank u so much man, will be needing you in the future lol

[@raghavbhatia3231]

Very helpfull sir.....

[@donny5429]

3:10 that sound

[@isabellestables5416]

I learnt a lot, thank you

[@sarah821]

Can I change an inverse(not a function) to a function by any way?

[@drterminator5082]

Yeah find the inverse of the inverse

[@vishgouravelli4264]

Thanks

[@mereditha6597]

Not all heroes wear capes.

[@blisterycrane6963]

i watching this now, cause i just stuffed my functions test.

[@jillmont3342]

THANK U

[@Siphephelomaseko9]

y = 1−2 √ x +3

[@ComedyGlor]

so can you not tell without drawing the graph? Say if you only have the equation, would you have to draw the function to know if it has an inverse?

[@esterhango2104]

No. Just check if that function is injective (one-to-one) . If it is then it does have an inverse😊

[@ComedyGlor]

Ester Hango thanks but how do you do that?

[@esterhango2104]

@@ComedyGlor You can start by letting xx' be the domains of the function. What you do is equate whatever function you got to itself...and then on one side you substitute x the other x' and then you do some mathematical manipulations ... If in the end you have x=x' then that function is injective and have an inverse I hope am clear tho. Otherwise just watch a KZbin vid on injectivity.

[@ComedyGlor]

Ester Hango ah okay thanks very much dearie

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which grade?

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goat teacher.

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[@brianmclogan]

Appreciate it

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[@brianmclogan]

happy to be able to help!

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[@juol2702]

HAHA woah it is cool seeing you biting the cap of the marker HAHAHA

[@lizhao810]

did you say.first function has no inverse?

[@brianmclogan]

it has an inverse, but the inverse is not a function

[@adebayosodiq5344]

because it failed horizontal line test

[@khalidashzz]

thx a lot 😍😍😍

[@brianmclogan]

happy to help

[@alexrode7858]

the speed of your dotted lines tho

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[@brianmclogan]

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5:58 / 7:31

[@brianmclogan]

What

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[@brianmclogan]

you are very welcome!

[@hussainshivaan419]

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[@brianmclogan]

you are very welcome!