Functions Revision Worksheet Q2

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

\(\mathrm{f}\left( x \right)=\sqrt{x+4}\), \(x\in \mathbb{R}\), \(-3\le x\le 5\)

\(\mathrm{g}\left( x \right)=2{{x}^{2}}-3\), \(x\in \mathbb{R}\), \(x\le 47\)

1. Find a simplified expression for \(\mathrm{gf}\left( x \right)\).
2. Determine the domain and range of \(\mathrm{gf}\left( x \right)\).