This applet shows how finding the inverse of f(x) is equivalent to tracing the locus of all points (f(x),x) for any function f(x). It has a nice tracing feature and allows for any function to be inputted. It also has the option of graphing reciprocal functions in order to show all 3 kinds of trig functions (original, inverse, reciprocal) on the same axes.
Drag the arrow on the x-axis.