first off, sorry for asking such a trivial question. I am going over the book Intermediate algebra from the AoPS series, and can't seem to figure out why my solution is wrong.
Function $\textit{f(x)} = \frac{cx}{2x+3}$ satisfies $(f\circ f)(x)=x$ for $x=\mathbb{R}\setminus \left\{ -\frac{3}{2}\right\} $.
Find $c$.
To me it seems quite obvious that expecting $c = 0 \rightarrow (f\circ f)(x) = \frac{c^{2}x}{2cx+6x+9} = \frac{x}{6x+9}$, thus making it undefined at $x = -\frac{3}{2}$ However, it appears that the correct answer is $c = -3$ https://artofproblemsolving.com/wiki/index.php/1980_AHSME_Problems/Problem_14
Thanks for your help.
P.S. I am sorry, for any mistakes made in the expressions.