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Function & Inverse Function Composition Action!

In the applet below, g is a function. The graph of its inverse, f, is shown in gray. What relationship does this applet graphically illustrate about a function and its inverse?
Note: Not every function has an inverse relation that is also a function. The principle you dynamically see illustrated here (with related notation) technically holds true for functions that are invertible (i.e. functions for which an inverse function actually exist. (For further information, visit this applet.) Can you form any conclusion about the relationship between any relation and its inverse relation?