Chapter 2 - Functions - 2.5 Preview of Composite and Inverse Functions - Exercises and Problems for Section 2.5 - Exercises and Problems - Page 102: 27

$f^{-1}(P)=\frac{P}{3-2 P}$

Since $P=\frac{3 x}{2 x+1}$, solving for $x$ gives $$ \begin{aligned} \frac{3 x}{2 x+1} & =P \\ 3 x & =2 x P+P \\ 3 x-2 x P & =P \\ x(3-2 P) & =P \\ x & =\frac{P}{3-2 P} \\ f^{-1}(P) & =\frac{P}{3-2 P} \end{aligned} $$