3. The functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } ( x ) \equiv 6 x - 1 , \quad x \in \mathbb { R } ,
& \mathrm {~g} ( x ) \equiv \log _ { 2 } ( 3 x + 1 ) , \quad x \in \mathbb { R } , \quad x > - \frac { 1 } { 3 } .
\end{aligned}$$
- Evaluate \(\mathrm { gf } ( 1 )\).
- Find an expression for \(\mathrm { g } ^ { - 1 } ( x )\).
- Find, in terms of natural logarithms, the solution of the equation
$$\mathrm { fg } ^ { - 1 } ( x ) = 2$$