How can I draw dots in a rooted tree structure graph?

Question

I wrote this code but I would like to add dots between the points to indicate that there are more points between the points I draw.

\documentclass[border=3.141592]{standalone}
\usepackage{forest}
\usetikzlibrary{arrows.meta}

\begin{document}
\begin{forest}
  for tree={
    edge = {Stealth-},
    grow = north
            }
[ $e(x)$
   [$\begin{matrix}
       \vdots\\
       f_{n_f}^{-1}(e(x))
   \end{matrix}$]
    [$\begin{matrix}
        \vdots \\
        f_{2}^{-1}(e(x))
    \end{matrix}$]
    
    [$f_{1}^{-1}(e(x))$,
        [$\begin{matrix}
          \vdots\\
          f_{n_f}^{-1}(f_{2}^{-1}(e(x)))
      \end{matrix}$]  
       [$\begin{matrix}
          \vdots\\
          f_{2}^{-2}(e(x))
      \end{matrix}$]
      [$\begin{matrix}
          \vdots\\
        f_{1}^{-1}(f_{2}^{-1}(e(x)))
      \end{matrix}$]
    ]
]
\end{forest}
\end{document}

The graph should look like this:

Can someone please help me?