(a) Functions \(f\) and \(g\) are such that, for \(x\in\mathbb R\), \(f(x)=x^2+3\) and \(g(x)=4x-1\).

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

(ii) Solve \(fg(x)=4\).

(b) A function \(h\) is such that \(h(x)=\dfrac{2x+1}{x-4}\), for \(x\in\mathbb R\), \(x\neq4\).

(i) Find \(h^{-1}(x)\) and state its range.

(ii) Find \(h^2(x)\), giving your answer in its simplest form.