1980 AMC 12 Question 14

If $c$ is a constant and the function $f$ defined by $$
\begin{gathered} f(x)=\frac{cx}{2x+3},\\ x\ne-\frac32, \end{gathered}
$$ satisfies $f(f(x))=x$ for all real numbers $x$ except $-\frac32,$ then $c$ is