Determine whether the statement is true or false. Explain your answer.
$$
\begin{array}{l}{\text { If } \lim _{x \rightarrow a^{-}} f(x) \text { and } \lim _{x \rightarrow a^{+}} f(x) \text { exist, then so does }} \\ {\lim _{x \rightarrow a} f(x)}\end{array}
$$