Answer
(a)$$\mathbb{R} - \{ -2 \}$$
(b)$$\mathbb{R}- \{ -2, 0 \}$$
Work Step by Step
To answer this question, we exclude the points $c$ for which $\lim_{x \to c} f(x)$ does not exist from the set of all real numbers.
(a)
$\lim_{x \to -2}f(x)$ does not exist since when $x$ approaches $-2$ from the left and right, the function approaches $0$ and $2$, respectively.
For the other points, the function has a limit at those points since the definition of limit clearly holds at those points.
(b)
$\lim_{x \to -2}f(x)$ does not exist since when $x$ approaches $-2$, the function $f(x)$ becomes unbounded and so does not approach a specific real number.
$\lim_{x \to 0}f(x)$ does not exist since when $x$ approaches $0$ from the left and right, the function approaches $0$ and $5$, respectively.
For the other points, the function has a limit at those points since the definition of limit clearly holds at those points.
