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:

Evaluating Functions:

Function Operations:

Increasing and Decreasing Functions:

Relative Maximum & Minimum Values:

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Relations and Functions:

Domain and Range From a Graph:

How To Find The Domain of a Function:

Average Rate of Change of a Function:

The Difference Quotient of a Function:

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Evaluating Piecewise Functions:

Graphing Piecewise Functions:

Composite Functions:

How To Evaluate Composite Functions:

Composite Functions - Data Table:

Comp. of 3 Functions - Data Table:

Decomposing Functions:

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Introduction to Inverse Functions:

How To Find The Inverse of a Function:

Verifying Inverse Functions:

Horizontal Line Test - 1 to 1 Functions:

Vertical Line Test:

Graphing Inverse Functions:

Composite and Inverse Functions:

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Even and Odd Functions:

Transformations of Functions:

Linear Functions:

Functions and Graphs - Problems:

Functions - Test Review:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

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[CR]

Wow! You make the concepts clear and understandable behind the "madness" of math. I really enjoy watching your videos, esp when I struggle. You help by setting a foundational understanding to functions. Just finished watching your multiplicity video and now I get it. Thank you. I wish you were the video instructor on our Moer portal for math!

[ethananderson]

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[TomsLab]

Weird, only 12 hours ago I had math class and this is what the lesson was about.

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[kkradhakrishnan]

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[georgesadler]

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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.

[ironmatt]

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[andrewgentle]

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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[aleksandarristoski]

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)

[zch]

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