IL-GILLIS 1997 Problem 4

Let $f : [0,1] \to [0,1]$ be a continuous, strictly increasing function such that $f(0) = 0$ and $f(1) = 1$ . Prove that $$f\left(\frac{1}{10}\right) + f\left(\frac{2}{10}\right) +...+f\left(\frac{9}{10}\right) +f^{-1}\left(\frac{1}{10}\right) +...+f^{-1}\left(\frac{9}{10}\right) \le \frac{99}{10}$$