If f(x) = l x, ; ; when , , 0 < x < 1/2 1, ; ; ; when , , x = 1/2… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}x,\;\;{\rm{when\,\,}}0 < x < 1/2\\1,\;\;\;{\rm{when\,\, }}x = 1/2\\1 - x,{\rm{when}}\;{\rm{1/2}} < x < {\rm{1}}\end{array} \right.$, then

A
$\mathop {\lim }\limits_{x \to 1/2 + } f(x) = 2$
B
$\mathop {\lim }\limits_{x \to 1/2 - } f(x) = 2$
C
$f(x)$is continuous at $x = \frac{1}{2}$
✓
$f(x)$is discontinuous at $x = \frac{1}{2}$

✓

Answer

Correct option: D.

$f(x)$is discontinuous at $x = \frac{1}{2}$

d
(d) Since $\mathop {\lim }\limits_{x \to 1/2} \,f(x) \ne f\left( {\frac{1}{2}} \right)$.

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