Question

$$(Fog)(x)=(9g(x))=2x-3$$

Evaluate (complex solution)

$Fgox=9gx\text{ and }9gx=2x-3$

Solve for x

$\left\{\begin{matrix}x=\frac{3}{2}=1.5\text{, }&g=0\\x=-\frac{3}{9g-2}\text{, }&F=\frac{9}{o}\text{ and }o\neq 0\text{ and }g\neq \frac{2}{9}\end{matrix}\right.$

Solve for o

$\left\{\begin{matrix}o=\frac{9}{F}\text{, }&F\neq 0\text{ and }g=\frac{2}{9}-\frac{1}{3x}\text{ and }x\neq 0\\o\in \mathrm{R}\text{, }&x=\frac{3}{2}\text{ and }g=0\end{matrix}\right.$