There is an interesting relationship between the domain and range values of
a function f and those of the inverse function. The connection is directed
related to the fact that there are corresponding points in the graph f and
the graph of 
that have their coordinates switched. If (x,y) is in
the graph of f then (y,x) is in the graph of . This says that
the domain and range values must be switched. That is, the values in the
domain of are the range values of f, while the range values of are the domain values of f. Of course, this must be the case since
while 
but thinking about the
graphs gives a nice geometric interpretation. Look below at the graphs of 
with domain 
and range 
(shown in red) and its inverse 
with domain 
and range 
(shown in blue).
