v-1(r) is the inverse function in this case, you just need to solve the equation for r, in which case you get:
r = sqrt( 0.16 - v(r)/18500)
Now simply replace v-1(r) with r, and r with v-1(r)
v-1(r) = sqrt( 0.16 - r/18500)
You only have to be careful with the limits in which these kind of systems are set. For example, here you know that velocity varies with the distance from the center, but you have a 0.4 cm radius here, where at 0cm you get the maximum speed and at 0.4 cm you get the minimum speed which is zero. If you don't set the limits as the system working between 0 and 0.4cm, then you will get negative speeds for radius bigger than 0.4, which makes no sense as you know there's no bigger radius possible and you will verify that because you will be getting the square root of a negative number after you solve for r and replace with the values of r > 0.4cm.
Hope it helped.
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