Galaxy Rotation Curves and Mass Discrepancy

[redtree]

I apologize for the simple question, but I am trying to understand the Mass Discrepancy-Acceleration Relation and its relationship to $\mu(x)$ (from https://arxiv.org/pdf/astro-ph/0403610.pdf).

The mass discrepancy, defined as the ratio of the gradients of the total to baryonic gravitational potential, can be described by a simple function of centripetal acceleration:

$D(x) = \frac{\Phi'}{\Phi'_{b}}$

Where $x = a/a0$ and $D(x)$ is the inverse of the following equation:

$\mu(x) = \frac{x}{\sqrt{1+x^2}}$

It's not clear to me how $D(x)$ is the inverse of the equation $\mu(x) = \frac{x}{\sqrt{1+x^2}}$.

For example, how would one substitute $\mu(x)$ for $D(x)$?

 

[haruspex]

I apologize for the simple question, but I am trying to understand the Mass Discrepancy-Acceleration Relation and its relationship to $\mu(x)$ (from https://arxiv.org/pdf/astro-ph/0403610.pdf).

The mass discrepancy, defined as the ratio of the gradients of the total to baryonic gravitational potential, can be described by a simple function of centripetal acceleration:

$D(x) = \frac{\Phi'}{\Phi'_{b}}$

Where $x = a/a0$ and $D(x)$ is the inverse of the following equation:

$\mu(x) = \frac{x}{\sqrt{1+x^2}}$

It's not clear to me how $D(x)$ is the inverse of the equation $\mu(x) = \frac{x}{\sqrt{1+x^2}}$.

For example, how would one substitute $\mu(x)$ for $D(x)$?

If it means merely that D() is the inverse function of $\mu(x)$ then that would be $D(x)=\frac x{\sqrt{1-x^2}}$.