If f(x) = l 1 + x, ; when , , x 2 5 - x, , when , , ,x 3 ., then - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}1 + x,\;{\rm{when\,\, }}x \le 2\\5 - x,\,{\rm{when \,\,}}\,x \le 3\end{array} \right.$, then

✓
$f(x)$ is continuous at $x = 2$
B
$f(x)$ is discontinuous at $x=2$
C
$f(x)$ is continuous at $x = 3$
D
None of these

✓

Answer

Correct option: A.

$f(x)$ is continuous at $x = 2$

a
(a) $\mathop {\lim }\limits_{x \to 2 - } f(x) = 3,\,\mathop {\lim }\limits_{x \to 2 + } \,f(x) = 3$ and $f(2)=3 $.

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