It is given that \(\mathrm f(x)=2\ln(3x-4)\), for \(x>a\), and that \(\mathrm f^{-1}\) exists.
Find the least possible value of \(a\).[1]
For your value of \(a\), find the range of \(\mathrm f\).[1]
For your value of \(a\), find an expression for \(\mathrm f^{-1}(x)\).[2]
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.[4]