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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If $f(x)=\left\{\begin{array}{ll}x, & \text { if } x \leq 1 \\ 7, & \text { if } x>1\end{array}\right.$ then at $x=1$
  • A
    $f$ is continuous
  • B
    $\lim _{x \rightarrow 1^{-}} f(x)=7$
  • C
    $\lim _{x \rightarrow 1^{+}} f(x)=1$
  • ✓
    $f$ is discontinuous
✓

Answer

Correct option: D.
$f$ is discontinuous
(d) $: f(1)=1$
$\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1} x=1, \lim _{x \rightarrow 1^{+}} f(x)=\lim _{x \rightarrow 1} 7=7$
Since, $f(1) \neq \lim _{x \rightarrow 1^{+}} f(x)$
$\therefore \quad f$ is discontinuous at $x=1$

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