If f (x)= r ^ -1 |x| ; when x 0 0 ; when x=0 ., then - Vidyadip

MCQ

If $f (x)=\left\{\begin{array}{r}\sin ^{-1}|x| \text {; when } x \neq 0 \\ 0 \text {; when } x=0\end{array}\right.$, then

A
$\lim _{x \rightarrow 0^{+}} f(x) \neq 0$
B
$\lim _{x \rightarrow 0^{-}} f(x) \neq 0$
✓
$f (x)$ is continuous at $x=0$
D
$f (x)$ is not continuous at $x=0$

✓

Answer

Correct option: C.

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

(C)
$\lim _{x \rightarrow 0} f(x)=\sin ^{-1}(0)=0=f(0)$
$\therefore \quad f (x)$ is continuous at $x=0$.

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