Mathematica - distance between two curves

Question

I am trying to compute the distance between these two curves. I have tried it like this FindMinimum[Norm[f[x] - q[x]], {x, 0.2}], but according to the automatic evaluation of my university this is incorrect.

a = 1.99435 
r = 1
f[x_] := Cos[Sqrt[8 Pi*ArcSin[x]]] + a 
q[x_] := -r*Sin[ArcCos[(x - 1)/r]] + 1.5;

Here's a picture: blue -> f[x], orange -> q[x]