MathNet 2009-part-01 — 175 problems (EN–VI) Question 118

Suppose that $f(x) = \frac{x}{\sqrt{1+x^2}}$ and $f^{(n)}(x) = f[f[f\dots f(x)]]$. Then $f^{(99)}(1) = \underline{\hspace{2cm}}$.