If f(x) = l 1 + x^2 , , , , when , , ,0 x 1 1 - x , , ,, when , ,… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}1 + {x^2},\,\,\,{\rm{when\,\,}}\,0 \le x \le 1\\1 - x\,\,\,,{\rm{when\,\,}}\,\,x > 1\end{array} \right.$, then

A
$\mathop {\lim }\limits_{x \to {1^ + }} f(x) \ne 0$
B
$\mathop {\lim }\limits_{x \to {1^ - }} f(x) \ne 2$
✓
$f(x)$ is discontinuous at $x = 1$
D
None of these

✓

Answer

Correct option: C.

$f(x)$ is discontinuous at $x = 1$

c
(c) $\mathop {\lim }\limits_{x \to 1 + } f(x) = 0$ and $\mathop {\lim }\limits_{x \to 1 - } \,\,f(x) = \,\,1 + 1 = 2$

Hence $f(x)$ is discontinuous at $x = 1$.

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