2005 AMC 12A Problems/Problem 20

Solution

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For the two functions f(x)=2x (0<=x<=1/2) and f(x)=2-2x (1/2<x<=1),we can see that as long as f(x) is between 0 and 1, x will be in the right domain. Therefore, we don't need to worry about the domain of x. Also, every time we change f(x), the final equation will be in a different form and thus we will get a different value of x. Every time we have two choices for f(x) and altogether we have to choose 2005 times. 2*2*2...2=2^2005