2014 TYS

The function \(\mathrm{f}\) is defined by

\(\mathrm{f}:x\mapsto \frac{1}{1-x}\), \(x\in \mathbb{R}\), \(x\ne 1\), \(x\ne 0\).

1. Show that \({{\mathrm{f}}^{2}}\left( x \right)={{\mathrm{f}}^{-1}}\left( x \right)\). [4]
2. Find \({{\mathrm{f}}^{3}}\left( x \right)\) and \({{\mathrm{f}}^{2020}}\left( x \right)\) in simplest form. [3]