It is given that \(\mathrm{f}(x)=2\ln(3x-4)\), for \(x\gt a\), and that \(\mathrm{f}^{-1}\) exists.

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

(b) For your value of \(a\), find the range of \(\mathrm{f}\).

(c) For your value of \(a\), find an expression for \(\mathrm{f}^{-1}(x)\).

(d) It is given that the equation \(\mathrm{f}(x)=\mathrm{f}^{-1}(x)\) has two roots. For your value of \(a\), sketch the graphs of \(y=\mathrm{f}(x)\) and \(y=\mathrm{f}^{-1}(x)\) on the axes. Label each graph. State the intercepts of each graph with the axes. State the equations of any asymptotes.