The functions \(f\) and \(g\) are defined by

\(f(x)=\operatorname{sec} x,\qquad \frac{\pi}{2}\lt x\lt \frac{3\pi}{2},\)

and

\(g(x)=3(x^2-1),\qquad x\in\mathbb R.\)

(a)(i) State the range of \(f\).

(a)(ii) Solve \(f^{-1}(x)=\frac{2\pi}{3}\).

(a)(iii) Given that \(gf\) exists, state the domain of \(gf\).

(a)(iv) Solve \(gf(x)=1\).

(b) The function \(h\) is defined by

\(h(x)=\ln(4-x),\qquad x\lt 4.\)

Sketch, on the same diagram, the graphs of \(y=h(x)\) and \(y=h^{-1}(x)\), showing clearly any asymptotes and any intersections with the axes.