The functions \(f\) and \(g\) are defined by \(f(x)=5x-2\) for \(x\gt 1\), and \(g(x)=4x^2-9\) for \(x\gt 0\).

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

(ii) Find the domain of \(gf\).

(iii) Showing all your working, find the exact solutions of \(gf(x)=45\).

(b) The function \(h\) is defined by \(h(x)=\sqrt{x^2-1}\) for \(x\leq-1\).

(i) State the geometrical relationship between the graphs of \(y=h(x)\) and \(y=h^{-1}(x)\).

(ii) Find an expression for \(h^{-1}(x)\).