The inverse of a function is when all of the x and y coordinates are switched.
Example: The inverse of (1,2) (2,4) (3,6) is (2,1) (4,2) (6,3)
To find the inverse of a function you must switch the x and y variable and then solve for y. This is denoted by 
. The domain of 
must be equal to the range of , and the range of must be equal to the domain of .
Example: If =x+4 "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
then =x-4 "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
To verify that you found the inverse of the function you can compose one to the other and it should equal x. If it doesn't then you did something wrong.
Example: )=f(x-4)=(x-4)+4=x "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
The graph of a function and its inverse are reflected across the line 
.
Example: The red graph is =3x+3 "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
and the green graph is =(x-3)/3 "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
.
Not all functions have inverses that are functions.
Example:
The red graph is =x^2 "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
The green graph is the inverse which is =\pm%20\sqrt{x} "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
The inverse if the red graph (green graph) is not a function because it doesn't pass the vertical line test.
Who ever wrote this is really smart.
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