I have the following function:
$$ f(x)= c_1\cdot c_2\cdot x\cdot \arctan\left(c_2\cdot x\right)-\frac{1}{2}\cdot c_1\cdot \ln\left(1+c_2^2\cdot x^2\right) $$
with $c_1=0.003$ and $c_2=150$ constants and $x \in [-0.035,0.035]$. The function represents a line, that when revolved around $y$ gives the surface of a mirror.
I would like to find the radius of the mirror from the axis of revolution (i.e. $x$-value in 2D) as a function of the height (i.e. $y$ or $f(x)$). The way I thought of approaching this problem is by inverting the function, however this doesn't seem to be possible.
What would be a good way to approach this problem?