Looking at the examples in the documentaion you could do the following:

g = InverseFunction[Function[{r,b,q},\[Rho]Asymp[r,b,q]],1,3]

which gives the inverse of \[Rho]Asymp[r,b,q], a function of 3 arguments, with respect to it's first argument r. Evaluation is then

g[1,2,3]
(*out:*) Sqrt[2]

The function g may now be used as a usual function.

Looking at the examples in the documentaion you could do the following:

g = InverseFunction[Function[{r, b, q}, ρAsymp[r, b, q]], 1, 3]

which gives the inverse of ρAsymp[r, b, q], a function of 3 arguments, with respect to it's first argument r. Evaluation is then

g[1, 2, 3]

Sqrt[2]

The function g may now be used as a usual function.