When the user presses a close Button that I created, some tasks are performed before exiting. However, if the user clicks on the [X] button in the top-right of the window to close the window, I cannot perform these tasks. 
How can I override what happens when the user clicks [X] button?
The command you are looking for is wm_protocol, giving it "WM_DELETE_WINDOW" as the protocol to bind to. It lets you define a procedure to call when the window manager closes the window (which is what happens when you click the [x]).
Overriding Tkinter "X" button control (the button that close the window)