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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
Function $f (x)=\left\{\begin{array}{cc}x-1, & x<2 \\ 2 x-3, & x \geq 2\end{array}\right.$ is continuous
  • ✓
    for all real values of x
  • B
    only for x = 2
  • C
    for all real values of x when x $\neq$ 2
  • D
    none of these
✓

Answer

Correct option: A.
for all real values of x
(A)
For $x<2, f (x)=x-1$
Since f is a polynomial function, it is continuous for all $x<2$.
For $x>2, f (x)=2 x-3$
Since f is a polynomial function, it is continuous for all $x>2$.
$\lim _{x \rightarrow 2^{-}} f (x)=\lim _{x \rightarrow 2}(x-1)=1$
$\lim _{x \rightarrow 2^{+}} f(x)=\lim _{x \rightarrow 2}(2 x-3)=1$
$f(2)=1$
$\therefore f (x)$ is continuous for all real values of $x$.

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