Functions Q2

The functions \(\mathrm{f}\) and \(\mathrm{g}\) are defined by

\(\mathrm{f}\left( x \right)={{x}^{2}}\), \(x\in \mathbb{R}\), \(x\ge 1\)

\(\mathrm{g}\left( x \right)=x-6\), \(x\in \mathbb{R}\), \(7\le x\le 10\).

1. Find the domain and range of \(\mathrm{fg}\left( x \right)\).
2. Show the following equation has no solutions
   \(\mathrm{fg}\left( x \right)={{\mathrm{g}}^{-1}}\left( x \right)\).