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]

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[@DavidStorm03]

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...

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[@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.

[@hanifrafli4736]

1:49 very satisfying sounds of whiteboard markers

[@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!

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[@brianmclogan]

happy to be able to help you out William

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[@brianmclogan]

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[@JamesBrodski]

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[@brianmclogan]

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[@brianmclogan]

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[@brianmclogan]

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[@brianmclogan]

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Thanks

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[@brianmclogan]

happy to help

[@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?

[@nurulwahida9049]

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[@blisterycrane6963]

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

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[@_____758]

thank goodness. i get it now

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[@user-bp5mg4bv2b]

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

[@user-gp2bh6jh3k]

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[@thomasf915]

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[@brianmclogan]

happy to be able to help!

[@sarah821]

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

[@drterminator5082]

Yeah find the inverse of the inverse

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goat teacher.

[@Siphephelomaseko9]

y = 1−2 √ x +3

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[@user-jl4ud4yn9c]

which grade?

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3:10 that sound

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I finally understand

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[@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

[@fr0iler578]

Thanks!😂😂

[@brianmclogan]

you are very welcome!

[@alexrode7858]

the speed of your dotted lines tho

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[@brianmclogan]

😍

[@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

[@user-in6qc4gx8g]

5:58 / 7:31

[@brianmclogan]

What