Find all the discontinuities of $f ( x ) = \left\{ \begin{array} { c c }
2 & \text { if } x \leq - 1 \
\frac { 1 } { x } & \text { if } - 1

Question

Find all the discontinuities of $f ( x ) = \left\{ \begin{array} { c c } 
2 & \text { if } x \leq - 1 \
\frac { 1 } { x } & \text { if } - 1 < x < 1 \
2 x - 1 & \text { if } x \geq 1
\end{array} \right.$
A) 0
B) -1
C) 0 and -1
D) f is continuous everywhere.

Quizplus · Accepted Answer

The function is discontinuous at $x = -1$ because the left-hand limit does not equal the right-hand limit. It is also discontinuous at $x = 0$ because $\frac{1}{x}$ is undefined at $x = 0$.

Find All the Discontinuities Of A) 0 B) -1 C) 0 and -1 D) F

Find All the Discontinuities Of A) 0
B) -1
C) 0 and -1
D) F