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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
The function $f(x)=\frac{4-x^2}{4 x-x^3}$ is
  • A
    discontinuous at only one point
  • B
    discontinuous exactly at two points
  • ✓
    discontinuous exactly at three points
  • D
    None of these
✓

Answer

Correct option: C.
discontinuous exactly at three points
(C)
$f (x)=\frac{4-x^2}{x\left(4-x^2\right)}=\frac{4-x^2}{x(2+x)(2-x)}$
Since $f (x)$ does not exist at $x=0,2,-2$.
∴ there are three points of discontinuity.

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