Let a function $\text{⨍ }$ defined by $\text{⨍ (x)=}\frac{\mathrm{x}-\left|\mathrm{x}\right|}{\mathrm{x}}$ for $\mathrm{x}\ne 0$ and $\text{⨍(0)=2.}$ then $\text{⨍ }$ is

$$\begin{gathered} \text{⨍ (x)=}\frac{\mathrm{x}-\left|\mathrm{x}\right|}{\mathrm{x}}\text{=}\left\{\begin{array}{l}0 if x>0\\ 2 if x=0\\ 2 if x<0\end{array}\right.\text{since }\left|x\right|\text{=}\left\{\begin{array}{ll}x& if x\ge 0\\ -x& if x<0\end{array}\right. \\ \text{∴}\underset{x\to 0}{\lim }\text{f}\left(x\right)\text{ does not exists} \\ \Rightarrow f\left(x\right) is discontinuous at x=0 \end{gathered}$$