The function f ( x ) = { 1 , if x 0 2 , if x = 0 is not continuous at:

Question

The function $f (x) =$ ${\begin{matrix} 1, & if x \neq 0 \\ 2, & if x = 0 \end{matrix}$ is not continuous at:

Smart Achievers · Accepted Answer

(1)

Ans. $x = 0$

Explanation:

$\lim_{x \to 0^{-}} f (x) = 1 = \lim_{x \to 0^{+}} f (x)$

and $f (0) = 2$

Here, $\lim_{x \to 0^{-}} f (x) = \lim_{x \to 0^{+}} f (x) \neq f (0)$

$∴$ $f (x)$ is not continuous at $x = 0$ .

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