Algebra 2 Inverse Functions
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If I Was You
Inverse Functions

 

 For some reason, 

 math people sometimes like to talk about the inverse of an equation.
 To write the inverse of an equation,
 all we do is swap the variables in the equation.
 So if we have:

 Y = 3X - 5

 
 The inverse is:

 X = 3Y - 5

 
 The usual practice is to turn this inverse equation
 into Y = stuff again.

 

 
 A cute thing happens with these inverse equations.
 If we start with the graph of the original equation,
 we can find the graph of the inverse equation
 by flipping the paper over on the diagonal line
 that runs from the lower left to the upper right.
 

 

 
 Some people say that an inverse equation
 is a reflection in a mirror that is placed along this diagonal line.
 

 

 That's all there is to it ...

 
 Example:
 Find the inverse of Y = X 4 + 3

 

 
 Example:
 Find the inverse of Y = X 2 - 4X + 6
 
 To keep this straight,
 first complete the square so there is only one X term in the equation.
 The number next to the X is -4, so that's what we need to use ...
 Remember the old A = 1, B = -4, C = 6 stuff?
 

 

 
 Now find the inverse (switch X and Y).
 

 X = (Y + 2)2 + 2

 
 and return the equation to the Y = (stuff) form ...

          

 

   copyright 2005 Bruce Kirkpatrick

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