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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
The value(s) of r for which the function
$f(x)=\left\{\begin{array}{cc}1-x , & x<1 \$1-x)(2-x) , & 1 \leq x \leq 2 \\3-x , & x>2\end{array}\right.$
fails to be continuous is (are)
  • A
    1
  • ✓
    2
  • C
    3
  • D
    All real numbers
✓

Answer

Correct option: B.
2
(B)
$\begin{array}{l}\lim _{x \rightarrow 1^{-}} f(x)=0, \lim _{x \rightarrow 1^{+}} f(x)=0 \text { and } f(1)=0\end{array}$
$\therefore \lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}} f(x)=f(1)$
$\therefore f (x)$ is continuous at $x=1$.
$\lim _{x \rightarrow 2^{-}} f (x)=0$ and $\lim _{x \rightarrow 2^{+}} f (x)=1$
$\therefore \lim _{x \rightarrow 2^{-}} f (x) \neq \lim _{x \rightarrow 2^{+}} f (x) =1$
$\therefore f (x)$ is not continuous at $x=2$.

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