6. The function f is defined by
$$\mathrm { f } ( x ) \equiv 3 - x ^ { 2 } , \quad x \in \mathbb { R } , \quad x \geq 0 .$$
- State the range of f.
- Sketch the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\) on the same diagram.
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state its domain.
The function g is defined by
$$\mathrm { g } ( x ) \equiv \frac { 8 } { 3 - x } , \quad x \in \mathbb { R } , \quad x \neq 3 .$$
- Evaluate \(\mathrm { fg } ( - 3 )\).
- Solve the equation
$$\mathrm { f } ^ { - 1 } ( x ) = \mathrm { g } ( x ) .$$