- The functions \(f\) and \(g\) are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 1 - 2 x ^ { 3 } , x \in \mathbb { R }
& \mathrm {~g} : x \mapsto \frac { 3 } { x } - 4 , x > 0 , x \in \mathbb { R }
\end{aligned}$$
- Find the inverse function \(\mathrm { f } ^ { - 1 }\).
- Show that the composite function gf is
$$\text { gf } : x \mapsto \frac { 8 x ^ { 3 } - 1 } { 1 - 2 x ^ { 3 } }$$
- Solve \(\operatorname { gf } ( x ) = 0\).
- Use calculus to find the coordinates of the stationary point on the graph of \(y = \operatorname { gf } ( x )\).