fa.functional analysis – Finding the “root” of a monotone function (in the sense of composition)

Let $f:(0,infty)rightarrow (0,infty) $ be a smooth and monotone function s.t $f(0)=0$. Let $Ninmathbb{N}$. Can we find a function $g: (0,infty) rightarrow (0,infty) $ s.t $gcirccdotscirc g$ ($g$ composed with itself $N$ times) equals $f$?

Can we say something about $g$‘s monotonicity? Its smoothness? I cannot come up with any basic answers. Thanks in advance to the helpers.