exp^(1/2)[ln^(1/2)[x]+1] - x

[tommy1729]

I was fascinated by the function exp^(1/2)[ln^(1/2)[x]+1] - x where x is a real > 0.
This function must be smaller than x.
But im puzzled by its growth rate on the real line and its singularity growth rate on the complex plane.
Maybe you guys know more.

Regards

tommy1729