2014 TYS

The function $\text{f}$ is defined by

$\text{f}:x\mapsto \frac{1}{1-x}, x\in \mathbb{R},x\ne 1,x\ne 0$ .

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