\textbf{111.} For which value of $a$, the function $f(x) = \begin{cases} \dfrac{3x-9}{x - \sqrt{x+2}} & ; \quad x > 2 \\ ax - 1 & ; \quad x \leq 2 \end{cases}$ is continuous on the set of real numbers?
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(1) $1.5$ \qquad
(2) $2$ \qquad
(3) $2.5$ \qquad
(4) $3$
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