6.
$$\mathrm { f } ( x ) = x ^ { 2 } - 2 x - 3 , x \in \mathbb { R } , x \geq 1$$
- Find the range of f .
- Write down the domain and range of \(\mathrm { f } ^ { - 1 }\).
- Sketch the graph of \(\mathrm { f } ^ { - 1 }\), indicating clearly the coordinates of any point at which the graph intersects the coordinate axes.
Given that \(\mathrm { g } ( x ) = | x - 4 | , x \in \mathbb { R }\),
- find an expression for \(\operatorname { gf } ( x )\).
- Solve \(\operatorname { gf } ( x ) = 8\).