8.
$$\mathrm { f } ( x ) \equiv 2 x ^ { 2 } + 4 x + 2 , \quad x \in \mathbb { R } , \quad x \geq - 1$$
- Express \(\mathrm { f } ( x )\) in the form \(a ( x + b ) ^ { 2 } + c\).
- Describe fully two transformations that would map the graph of \(y = x ^ { 2 } , x \geq 0\) onto the graph of \(y = \mathrm { f } ( x )\).
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state its domain.
- Sketch the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\) on the same diagram and state the relationship between them.