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I am to solve for $r(\rho)$ given the function,

 \[Rho]Asymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)]

This can be solved in a straightforward way by converting this into a quadratic equation and use Solve to find for the root corresponding to $r(\rho)$ for every value of $q$. But I have difficulty implementing the InverseFunction to this problem. Can someone help me with this? Also i want to scan $r(\rho)$ for all values of $q<1$, how can I implement this by using a Module? Thank you

I am to solve for $r(\rho)$ given the function,

ρAsymp[r_, b_, q_] := 
  1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)]

This can be solved in a straightforward way by converting this into a quadratic equation and use Solve to find for the root corresponding to $r(\rho)$ for every value of $q$. But I have difficulty implementing the InverseFunction to this problem. 

Can someone help me with this? Also, I want to scan $r(\rho)$ for all values of $q<1$, how can I implement this by using a Module?

I am to solve for $r(ρ)$ given the function,

 ρAsymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)]

This can be solved in a straightforward way by converting this into a quadratic equation and use Solve to find for the root corresponding to $r(ρ)$ for every value of $q$. But I have difficulty implementing the InverseFunction to this problem. Can someone help me with this? Also i want to scan $r(ρ)$ for all values of $q<1$, how can I implement this by using a Module? Thank you

I am to solve for $r(\rho)$ given the function,

 \[Rho]Asymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)]

This can be solved in a straightforward way by converting this into a quadratic equation and use Solve to find for the root corresponding to $r(\rho)$ for every value of $q$. But I have difficulty implementing the InverseFunction to this problem. Can someone help me with this? Also i want to scan $r(\rho)$ for all values of $q<1$, how can I implement this by using a Module? Thank you

I am to solve for $r(\rho)$ given the function,

 \[Rho]Asymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)]

This can be solved in a straightforward way by converting this into a quadratic equation and use Solve to find for the root corresponding to $r(\rho)$ for every value of $q$. But I have difficulty implementing the InverseFunction to this problem. Can someone help me with this? Also i want to scan $r(\rho)$ for all values of $q<1$, how can I implement this by using a Module? Thank you

I am to solve for $r(ρ)$ given the function,

 ρAsymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)]

This can be solved in a straightforward way by converting this into a quadratic equation and use Solve to find for the root corresponding to $r(ρ)$ for every value of $q$. But I have difficulty implementing the InverseFunction to this problem. Can someone help me with this? Also i want to scan $r(ρ)$ for all values of $q<1$, how can I implement this by using a Module? Thank you