Introduction to Inverse Functions

[@TheOrganicChemistryTutor]

Functions - Free Formula Sheet: bit.ly/3Ai8NZv Final Exams and Video Playlists: www.video-tutor.net/ Functions and Graphs: kzbin.info/www/bejne/kIWop2uFo6yUrtE Next Video: kzbin.info/www/bejne/aKvIiniuacqHmsU Transformations of Functions: kzbin.info/www/bejne/qqq0faNsrZJ6pbc Graphing Polynomial Functions: kzbin.info/www/bejne/qICylpmaprKpqqM

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[@EmpyreanLightASMR]

The end of this video is a bit confusing I think: f(x)=x^2 is a function. It passes the vertical line test. But it fails the horizontal line test. So it is not a one-to-one function (I had to look this part up elsewhere). The inverse is NOT a function, which he shows. f-1(x)=±√x has two answers, the positive √x and the negative √x, which means it's not a one-to-one function. When you plot both of these on the graph, together they fail the vertical line test. Btw, the horizontal line test is ONLY for the original f(x) function to test if its inverse would be a function. You don't use the horizontal line test after you've already drawn the inverse on the graph. That would just be crazy talk.

[@user-eu2mg8lw2t]

simply put, f(x)=x^2 is a function, it's inverse is not a function if f(x) passes the vertical line test it is a function if f(x) passes the horizontal line test it's inverse is a function

[@EmpyreanLightASMR]

@@user-eu2mg8lw2t Ha, yes, succinctly put. You should've seen my comment before I rewrote it entirely. I was so confused.

[@pkus]

@@user-eu2mg8lw2t agreed

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[@elimgarak7090]

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[@nandorsieben6660]

A function that is not one-to-one does not have an inverse. The plus or minus does not cure this problem.

[@connerallred7829]

Does anyone know how to make an inverse into an original function if I’ve got some points if x is this and f(x) is this?

[@sincerely_solvency1836]

I think you just switch x for y (look for the inverse) and solve to get y by itself. It’s the same as solving for the inverse of the inverse.

[@sincerely_solvency1836]

Basically do what he showed you but with the inverse it’s the same thing

[@ForStudying-w8q]

hey question about 2:06. I thought that in order to be a function each domain needed to have exactly one corresponding range but putting plus minus gives two domains which confused me

[@anniesina1235]

Yes, x square has two solutions. A function must be bijective (one to one and onto type function) function in order to have an inverse function. Hence x squared does not have an inverse function (somewhere near the end of the video he said x >= 0 so that can make sense). Other way to explain is that sqrt x does not exactly inverse the effect of the function because it gives both negative and positive outcomes

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[@aleksandarristoski2777]

I think there is a mistake with x^2 - 4 . You cannot have that since x+4 = y^2 means two answers. y^2 is always equal to two numbers. -/+ sqr(X+4)

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[@atomix2933]

I don't understand. Please elaborate further.

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​@@B6lpl can you please explain to me what he/she was trying to say? he/she didn't express his/her confusion specifically. That's why i am asking you

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[@cyrex-niaz7798]

6:49 the graph shows that+-✓x can't be a function on its self, Then is it a function itself when its a inverse function?

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[@andrewgentle8620]

For the bottom half of the sqrt x would that not turn it into a many-to-one function which you cant do with inverse functions

[@miahreynolds9713]

at 2:04 in the video, why did you use a square root? Is that the inverse operation of an exponent?

[@Bangtan_Vibes_7]

Isn't he supposed to do this? Cuz when we sqrt both the sides, we get the value of y which is +/-√x+4

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could you please make a playlist for only the function from the introduction to the last topic

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[@pkus]

2:00 here its mistake: x = y^2 - 4 => y^2 = x + 4 => y= rootover(x+4) or negative rootover(x+4)

[@Bangtan_Vibes_7]

He did the same tho

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[@jesuisravi]

how can f(x)= x^2 have an inverse?

[@dilawazranidilawazrani5549]

Right

[@abdulrahmannasser14]

@@dilawazranidilawazrani5549 Only then that he must tell you or assume that you know that √-x is not a real number and so the functions range does not include √-x and then function piece can be inverted without any problems.

[@eimaanahmad8839]

Square root

[@pkus]

it does not have inverse function as it failed with horizontal line test for y= x^2, but I think we can show what we can get x = y^2, rootover(y^2) = +-rootover(x), y = positive rootover(x), or negative rootover(x).

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[@the_green_cloud]

2:04 doesn't that not make it a function then?

[@NulliusInVerba8]

So should we always use the vertical line test for the function and the horizontal for the inverse ?

[@EmpyreanLightASMR]

He lost me at the very end, BUT to answer your question: Use the vertical line test on f(x) and if it passes, it's a function. But use the horizontal line test on that same f(x) line to determine if the inverse is a function. Once you've drawn the inverse onto the graph, then you go back to using the vertical line test on it. In other words, the horizontal is only used on f(x) to determine the inverse. Do not use the horizontal line test on the actual line drawn from f-1(x).

[@NulliusInVerba8]

@@EmpyreanLightASMR Nice and clear. Thanks a lot!

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[@mainaccount0411]

2:03 shouldn't it be +/- why didn't he add that its a square root

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[@m15hramathematics]

Mistake at 2:02 it should've been plus/minus square root of x+4 but anyways really helpful

[@bvagasky83]

He....he did put ±√x+4.... if you waited and watched a whole three more seconds later at 2:05

[@khelan1645]

Thanks ☺️

[@anthonywiggins9870]

Great Video!!....however I think you should clarify your language a bit. The inverse OF a function is not the same thing as the inverse function. The inverse of a function need not BE a function while the inverse function must be a function.

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[@irajasivadas4413]

You explain things clearly, but some of your examples are wrong. f(x) = x^2 - 4 is not a 1-1 function, therefore has no inverse. You should have noticed this when you took the square root of y^2 which gives two answers. If you limit the domain of f(x) = x^2 - 4 to [0, infinite) then it has an inverse.

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[@hafsaimtiaz5832]

In frst eg wht ws those points (2,7)????

[@pkus]

he just gave example inverse function work with point x,y = 2,7 for f(x) but it will become 7,2 for f'(x)

[@huynhthu1843]

1. how to find inverse function 2. how to know if 2 functions are inverse function of each other 3. the property of inverse function 4. how to draw the inverse function 5. how to know f(x) is a function? 6. how to know the inverse is a function

[@pabapaththandupitiya1313]

i think the first question is wrong. how is 3y-1 multiplied by x equals to 3xy-3x. i understand the 3xy part but how did the 3x happen? there is no 3 to multiply it with ? or maybe i am trippin

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What is domain and range I don't understand it

[@KimgQuadratic]

Domain is the values for "x" Range is the values for "y" Its used for arrow and mapping diagrams when you substitute the number into the function Example: (2) --> (y) 4x - 1 = y 2(4) - 1 = y 7 = y Therefore: (2) ---> 『y=4x-1』---> (7)

[@sanopann1896]

so confusing about how you explain to test the graph using vertical and horizontal line you said used a vertical line for the original function and horizontal line for inverse function ???????

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[@mukeshgupta7615]

Function y =Sinx fails horizontal line test , Does it mean inverse of Sin function doesnt exist , Any one can explain this please.

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Man i do not understand this part at all

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2nd Question's inverse function is wrong, in fact that function cant have an inverse function, cause its not a one to one function.... PL correct that

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