6. The function f is defined by
$$\mathrm { f } ( x ) \equiv 4 - \ln 3 x , \quad x \in \mathbb { R } , \quad x > 0 .$$
- Solve the equation \(\mathrm { f } ( x ) = 0\).
- Sketch the curve \(y = \mathrm { f } ( x )\).
- Find an expression for the inverse function, \(\mathrm { f } ^ { - 1 } ( x )\).
The function \(g\) is defined by
$$\mathrm { g } ( x ) \equiv \mathrm { e } ^ { 2 - x } , \quad x \in \mathbb { R }$$
- Show that
$$\operatorname { fg } ( x ) = x + a - \ln b$$
where \(a\) and \(b\) are integers to be found.