11. The functions \(f\) and \(g\) are defined by
$$\begin{array} { l l }
\mathrm { f } ( x ) = \frac { 3 } { 2 } \ln x & x > 0
\mathrm {~g} ( x ) = \frac { 4 x + 3 } { 2 x + 1 } & x > 0
\end{array}$$
- Find \(\operatorname { gf } \left( e ^ { 2 } \right)\) writing your answer in simplest form.
- Find the range of the function fg .
- Given that \(\mathrm { f } ( 8 )\) and \(\mathrm { f } ( 2 )\) are the second and third terms respectively of a geometric series, find the sum to infinity of this series, giving your answer in the form \(a \ln 2\) where \(a\) is rational.
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