If f (x)= r x-|x| x ; when x 0 2 ; when x=0 ., then - Vidyadip

MCQ

If $f (x)=\left\{\begin{array}{r}\frac{x-|x|}{x} ; \text { when } x \neq 0 \\ 2 ; \text { when } x=0\end{array}\right.$, then

A
$f (x)$ is continuous at $x=0$
✓
$f (x)$ is discontinuous at $x=0$
C
$\lim _{x \rightarrow 0} f(x)=2$
D
$\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{+}} f(x)$

✓

Answer

Correct option: B.

$f (x)$ is discontinuous at $x=0$

(B)
$\lim _{x \rightarrow 0^{-}} f (x)=1+1=2$
$\lim _{x \rightarrow 0^{+}} f(x)=0$
$\therefore \quad f (x)$ is discontinuous at $x=0$.

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