(iii) To express \(6x - x^2\) in the form \(a - (x-b)^2\), we complete the square:

\(6x - x^2 = -(x^2 - 6x)\)

\(= -(x^2 - 6x + 9 - 9)\)

\(= -(x-3)^2 + 9\)

Thus, \(6x - x^2 = 9 - (x-3)^2\).

(iv) To find \(h^{-1}(x)\), start with \(y = 6x - x^2\).

Rearrange to express \(x\) in terms of \(y\):

\(y = 9 - (x-3)^2\)

\((x-3)^2 = 9 - y\)

\(x-3 = \pm \sqrt{9-y}\)

Since \(x \geq 3\), we take the positive root:

\(x = 3 + \sqrt{9-y}\)

Thus, \(h^{-1}(x) = 3 + \sqrt{9-x}\).