Answer
$\frac{4}{3}$
Work Step by Step
We are sure that this function is continuous at all points except at x=3 ( as polynomial functions are continuous inside their interval).
f(x) is continuous at x=3 if and only if
$\lim\limits_{x \to 3^{+}}f(x)= \lim\limits_{x \to 3^{-}}f(x)= f(3)$
⇒$3^{2}-1= 2a\times3$
⇒8= 6a or a= $\frac{4}{3}$
