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Unformatted text preview: Participation credit problems October 8, 2010 Deadline: The day after the second test. For each of the following, an appropriate solution is a proof , i.e., you must give fully rigorous reasons for your answers. Saying yes or no is NOT su cient. Completing these problems will earn one participation credit. Please do all scratchwork on a di erent sheet, and only include a full, cleanly written solution on this sheet (i.e., no excessive erasing, scratching out, etc.). 1. This question has three parts: (a) In class I stated that the function f ( x ) = 0 is both even and odd. Is any other function both even and odd? Either give an example of a di erent function and show that it is both even and odd, or use the de nitions of even and odd function to show that, if f ( x ) is both even and odd, then f ( x ) must equal 0. (b) I can only think of one function f ( x ) with domain (- , ) which is its own inverse, i.e., f ( x ) = f- 1 ( x ) . What is the function? Show that it is in fact its own inverse. (Note: it is not....
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