Problem 5 omitted a piece of information. As it is, the answer is not unique, it could be 1 or it could be 1/793.

Choose a > 1. The following continuous function satisfies the desired property:

So if 793 is in the middle interval, then f(793) = 1/793. If 793 is not, then f(793) can be anything. The original problem was supposed to have the information that f(1000) = 1/1000. Interestingly enough, if a = 1 we get that f(x) = 1 works.

I gave points to solutions that were reasonable and possible. Sorry about that!

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