The one$-$to$-$one function $g$ is defined below.

$g(x)=\frac{9x}{8x-3}$

Find $g^{-1}(x),$ where $g^{-1}$ is the inverse of $g.$

Also state the domain and range of $g^{-1}$ in interval notation.

$($:$g^{-1}$:$(-,\frac{3}{8})(\frac{3}{8},]\}$