Answer
(a) $\lim\limits_{x \to 3^{-}}f(x)$ = 2
(b) $\lim\limits_{x \to 3^{+}}f(x)$ = 2
(c) $\lim\limits_{x \to 3}f(x)$ = 2
Work Step by Step
(a) In this case x $\leq$ 3, then $f(x)$ = x - 1.
$\lim\limits_{x \to 3^{-}}f(x)$ = $\lim\limits_{x \to 3^{-}}x-1$ = 3 - 1 = 2
(b) In this case x $\gt$ 3, then $f(x)$ = 3x - 7
$\lim\limits_{x \to 3^{+}}f(x)$ = $\lim\limits_{x \to 3^{+}}3x-7$ = 3$\times$3 - 7 = 2
(c) As $\lim\limits_{x \to 3^{+}}f(x)$ = $\lim\limits_{x \to 3^{-}}f(x)$ = 2, we conclude that $\lim\limits_{x \to 3}f(x)$ = 2
