It is given that
\(f(x) = \begin{cases}(1/2)(x - |x|), & \quad \text{when } x ≠ 0\text{}\\ 2, & \quad \text{when } x = 0 \text{} \end{cases} \)
Consider left hand limit at x = 0
Here the value of function at x = 0 is f(x) = 2
We get f(0) = 2
So
Therefore, f(x) is discontinuous at x = 0.