Answer
(a) 2
(b) -4
Work Step by Step
(a) If $f$ is left-continuous at $x=3$, then
$\lim\limits_{x \to 3^{-}}f(x)=f(3)$.
As $f(x)=2$ for $x\lt3,$ $\lim\limits_{x \to 3^{-}}f(x)=2$
$\implies f(3)=2$
(b) If $f$ is right-continuous at $x=3$, then
$\lim\limits_{x \to 3^{+}}f(x)=f(3)$.
As $f(x)=-4$ for $x\gt3,$ $\lim\limits_{x \to 3^{+}}f(x)=-4$
$\implies f(3)=-4$
