I am currently working with this hypergeometric function ${_2}F_1$,
$\rho(r)=\frac{2b}{1-q}(1-(\frac{b}{r})^{1-q})^{\frac{1}{2}}{_2}F_1(\frac{1}{2},1-\frac{1}{q-1},\frac{3}{2},1-(\frac{b}{r})^{1-q})$
I have just started learning and using Mathematica and I just want to ask if I can use Mathematica to construct and implement a simple routine to numerically invert the function $\rho(r)$ into $r(\rho)$? Note that $-\infty<q<1$, and $r,b>0$. Thanks in advance