The authors' investigation was concerned with the sufficient and necessary conditions under which one class of operational functions of the form: \begin{equation}abel{eq1} R(x)=\frac1{(lpha(x)s+\beta(x))^a}, \qquad ext{Re}\quad a>0 \end{equation} is continuous in the point $x_0$, in the sense of continuity which is defined by Mikusiński operational calculus. extsc{Theorem 1}. \emph{Suppose that}: \begin{itemize} ıem [(i)] \emph{$\alpha(x)$ and $\beta(x)$ are numerical, real, continuous functions on the interval $I=[c,d]$} ıem [(ii)] \emph{$c<x_0<d$ and $x_0$ is an isolated zero of the function $\alpha(x)$, $\alpha(x_0)=0$} ıem [(iii)] $\beta(x_0)\neq0$ \end{itemize} \emph{The necessary and sufficient condition for the operator function \eqref{eq1} to be continuous in $x=x_0$ is the existence of a neighborhood $V_0$ of the point $x_0$ in which $\gamma(x)=\frac{\beta(x)}{\alpha(x)}>0$ while $x\in V_0\backslash\{x_0\}$} This paper extends the results obtained in [6] and [7]. They follow from theorem 1 for $a=1$ and $a=1/n$.