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The function f is defined for all real values of \(x\) by
$$\mathrm { f } ( x ) = 2 - \sqrt [ 3 ] { x + 1 }$$
The diagram shows the graph of \(y = \mathrm { f } ( x )\).
- Evaluate \(\mathrm { ff } ( - 126 )\).
- Find the set of values of \(x\) for which \(\mathrm { f } ( x ) = | \mathrm { f } ( x ) |\).
- 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.
The equation of a curve is \(y = \left( x ^ { 2 } + 1 \right) ^ { 8 }\).