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Question
Prove that \[f\left( x \right) = \begin{cases}\frac{x - \left| x \right|}{x}, & x \neq 0 \\ 2 , & x = 0\end{cases}\] is discontinuous at x = 0
Solution
The given function can be rewritten as
(LHL at x = 0) =
Thus, f(x) is discontinuous at x = 0.
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