It is given that \(f(x)=5e^x-1\) for \(x\in\mathbb{R}\).

(i) Write down the range of \(f\).

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

It is given also that \(g(x)=x^2+4\) for \(x\in\mathbb{R}\).

(iii) Find the value of \(fg(1)\).

(iv) Find the exact solutions of \(g^2(x)=40\).