Suppose the red graph below is of f(x) and the green graph is of g(x).
A graph and its inverse will always intertwine symmetrically in this 
fashion because x and y are swapped (interchanged) in the inverse.



Notice the line that they are reflections about.  It is this dotted line
below:

  

That dotted line about which each is the reflection of the other is the
graph of the line y = x, because when you swap the letters in y = x,
you get x = y which is the same equation.  So that dotted line is the
ONLY function which is ITS OWN inverse.  All other functions and 
inverses are reflections of each other in that dotted line.  Notice 
that this line is the line which goes through the origin and goes up 
at a 45° angle.  Every point on that dotted line has the same x and y
coordinates, such as (3,3), (-5,-5), (1,1) etc.

Edwin