(a) The diagram shows the graph of \(y=f(x)\), where \(f\) is defined by

\(f(x)=\frac{3x}{\sqrt{5x+1}}\quad\text{for }0\leq x\leq3.\)

(i) Given that \(f\) is a one-one function, find the domain and range of \(f^{-1}\).

(ii) Solve the equation \(f(x)=x\).

(iii) Sketch the graph of \(y=f^{-1}(x)\).

(b) The functions \(g\) and \(h\) are defined by

\(g(x)=\sqrt[3]{8x^3+3}\quad\text{for }x\geq1, \qquad h(x)=e^{4x}\quad\text{for }x\geq k.\)

(i) Find an expression for \(g^{-1}(x)\).

(ii) State the least value of the constant \(k\) such that \(gh(x)\) can be formed.

(iii) Find and simplify an expression for \(gh(x)\).