A function \(f(x)\) is such that

\(f(x)=\ln(2x+3)+\ln4,\)

for \(x\gt a\), where \(a\) is a constant.

(a) Write down the least possible value of \(a\).

(b) Using your value of \(a\), write down the range of \(f\).

(c) Using your value of \(a\), find \(f^{-1}(x)\), stating its range.

(d) On the axes below, sketch the graphs of \(y=f(x)\) and \(y=f^{-1}(x)\), stating the exact intercepts of each graph with the coordinate axes. Label each of your graphs.