Question 17Let $f(x)=10^{10x},$ $g(x)=\log_{10}\!\left(\dfrac{x}{10}\right),$ $h_1(x)=g(f(x)),$ and $h_n(x)=h_1(h_{n-1}(x))$ for integers $n\ge2.$ What is the sum of the digits of $h_{2011}(1)?$$16{,}081$$16{,}089$$18{,}089$$18{,}098$$18{,}099$