Answer
The function is continuous when $a=7.$
Work Step by Step
$\lim\limits_{x\to1^-}f(x)=a(1^-)-4=a-4.$
$\lim\limits_{x\to1^+}f(x)=3(1^+)^2=3$
For the function to be continuous, $\lim\limits_{x\to1^+}f(x)=\lim\limits_{x\to1^-}f(x)\to$
$ a-4=3\to a=7.$
