(a)(i) Sketch the graph of \(y=|(x+3)(x-5)|\), showing the coordinates of the points where the curve meets the \(x\)-axis.

(a)(ii) Write down a suitable domain for the function \(f(x)=|(x+3)(x-5)|\) such that \(f\) has an inverse.

(b) The functions \(g\) and \(h\) are defined by

\(g(x)=3x-1\quad\text{for }x\gt 1, \qquad h(x)=\frac4x\quad\text{for }x\ne0.\)

(i) Find \(hg(x)\).

(ii) Find \((hg)^{-1}(x)\).

(c) Given that \(p(a)=b\) and that \(p\) has an inverse, write down \(p^{-1}(b)\).