(a) It is given that \(f(x)=3e^{-4x}+5\), for \(x\in\mathbb R\).

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

(ii) Find \(f^{-1}\) and state its domain.

(b) It is given that \(g(x)=x^2+5\) and \(h(x)=\ln x\), for \(x\gt 0\). Solve \(hg(x)=2\).