9709 P1 - Nov 2006 - Q10
734
The function f is defined by \(f : x \mapsto x^2 - 3x\) for \(x \in \mathbb{R}\).
(ii) Express \(f(x)\) in the form \((x-a)^2 - b\), stating the values of \(a\) and \(b\).
(iii) Write down the range of \(f\).
(iv) State, with a reason, whether \(f\) has an inverse.
The function \(g\) is defined by \(g : x \mapsto x - 3\sqrt{x}\) for \(x \geq 0\).
(v) Solve the equation \(g(x) = 10\).
