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f(x)=1010xg(x)=log10(x10)h1(x)=g(f(x))hn(x)=h1(hn−1(x)) \begin{aligned} f(x) & = & 10^{10x} \\ g(x) & = & \log_{10} \left ( \frac x {10} \right ) \\ h_1 (x) & = & g(f(x)) \\ h_n (x) & = & h_1 (h_{n-1} (x)) \\ \end{aligned} f(x)g(x)h1(x)hn(x)====1010xlog10(10x)g(f(x))h1(hn−1(x))
Denote the set functions above. Evaluate the sum of digits of h2011(1) h_{2011} (1) h2011(1).
Note- This is not original. Adapted from a Math contest.
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