10 The function f is defined by \(\mathrm { f } : x \mapsto x ^ { 2 } - 3 x\) for \(x \in \mathbb { R }\).
- Find the set of values of \(x\) for which \(\mathrm { f } ( x ) > 4\).
- Express \(\mathrm { f } ( x )\) in the form \(( x - a ) ^ { 2 } - b\), stating the values of \(a\) and \(b\).
- Write down the range of f .
- State, with a reason, whether f has an inverse.
The function g is defined by \(\mathrm { g } : x \mapsto x - 3 \sqrt { } x\) for \(x \geqslant 0\).
- Solve the equation \(\mathrm { g } ( x ) = 10\).