\textbf{114-} The function with the rule $f(x) = \begin{cases} |x| + [-x] & ; \ x \notin \mathbb{Z} \\ a & ; \ x \in \mathbb{Z} \end{cases}$, for which value of $a$, is continuous on the set of real numbers?
(Note: $[\ ]$ denotes the floor function.)
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(1) $-1$ \hfill (2) $1$ \hfill (3) $0$ \hfill (4) Always discontinuous
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