Introduction to Inverse Functions

This algebra video tutorial provides a basic introduction into inverse functions. it explains how to find the inverse function by switching the x and y variables. It also explains how to prove if two functions are inverses of each by checking to see if the composite functions of f(g(x)) and g(f(x)) are equal to x. In addition, it explains how to graph the inverse function around the line y=x. Finally, it highlights the difference between the vertical line test and the horizontal line test as it relates to one to one functions and inverse functions. The vertical line test tells if a relation is a function. The horizontal line test tells you if the function is one to one and if the inverse relation is a function.
Introduction to Functions:
• Functions - Vertical L...
Evaluating Functions:
• Evaluating Functions -...
Function Operations:
• Function Operations
Increasing and Decreasing Functions:
• Increasing and Decreas...
Relative Maximum & Minimum Values:
• Identifying The Relati...
_____________________________________
Relations and Functions:
• Relations and Function...
Domain and Range From a Graph:
• Domain and Range of a ...
How To Find The Domain of a Function:
• How To Find The Domain...
Average Rate of Change of a Function:
• Average Rate of Change...
The Difference Quotient of a Function:
• Difference Quotient
_____________________________________
Evaluating Piecewise Functions:
• Evaluating Piecewise F...
Graphing Piecewise Functions:
• Graphing Piecewise Fun...
Composite Functions:
• Composite Functions
How To Evaluate Composite Functions:
• How To Evaluate Compos...
Composite Functions - Data Table:
• How To Evaluate Compos...
Comp. of 3 Functions - Data Table:
• Composition of Three F...
Decomposing Functions:
• Decomposing Functions ...
_________________________________
Introduction to Inverse Functions:
• Introduction to Invers...
How To Find The Inverse of a Function:
• How To Find The Invers...
Verifying Inverse Functions:
• Verifying Inverse Func...
Horizontal Line Test - 1 to 1 Functions:
• Horizontal Line Test a...
Vertical Line Test:
• Vertical Line Test
Graphing Inverse Functions:
• Graphing Inverse Funct...
Composite and Inverse Functions:
• Composite Functions an...
__________________________________
Even and Odd Functions:
• Even, Odd, or Neither ...
Transformations of Functions:
• Transformations of Fun...
Linear Functions:
• Linear Functions
Functions and Graphs - Problems:
• Functions and Graphs |...
Functions - Test Review:
• Functions
______________________________________
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Full-Length Videos and Worksheets:
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[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/aKvIiniuacqHmsU Final Exams and Video Playlists: www.video-tutor.net/ Functions and Graphs: kzbin.info/www/bejne/kIWop2uFo6yUrtE 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.

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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)

[@C_V_V_N]

Yes thats right

[@atomix2933]

I don't understand. Please elaborate further.

[@Bangtan_Vibes_7]

​@@C_V_V_N 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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[@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

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[@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

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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.

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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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[@pursuegamer1735]

What is domain and range I don't understand it

[@bethelyemane6578]

How can we cancel 3 by 3 when there is addition??? , that def restricts it.

[@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

[@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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[@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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[@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)

[@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

[@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

[@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 ???????

[@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.

[@the_green_cloud]

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

[@mainaccount0411]

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

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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.

[@ayushmishra8144]

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

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

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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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