Give full details of the single transformation that transforms the graph of \(y = x ^ { 3 }\) to the graph of \(y = x ^ { 3 } - 8\).
The function f is defined by \(\mathrm { f } ( x ) = x ^ { 3 } - 8\).
Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
State how the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\) are related geometrically.