



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 
