(a) It is given that \(f:x\mapsto(3x+1)^2-4\), for \(x\geq a\), and that \(f^{-1}\) exists.

(i) Find the least possible value of \(a\).

(ii) Using this value of \(a\), write down the range of \(f\).

(iii) Using this value of \(a\), sketch the graphs of \(y=f(x)\) and \(y=f^{-1}(x)\), stating the intercepts with the coordinate axes.

(b) It is given that \(g(x)=\ln(2x^2+5)\), for \(x\geq0\), and \(h(x)=3x-2\), for \(x\geq0\).

Solve the equation \(hg(x)=4\), giving your answer in exact form.