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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
The function $f (x)=\frac{2 x^2+7}{x^3+3 x^2-x-3}$ is discontinuous for
  • A
    $x=1$ only
  • B
    $x=1$ and $x=-1$ only
  • ✓
    $x=1, x=-1, x=-3$ only
  • D
    $x=1, x=-1, x=-3$ and other values of $x$
✓

Answer

Correct option: C.
$x=1, x=-1, x=-3$ only
(C)
$f (x)=\frac{2 x^2+7}{x^2(x+3)-1(x+3)}=\frac{2 x^2+7}{\left(x^2-1\right)(x+3)}$
$=\frac{2 x^2+7}{(x-1)(x+1)(x+3)}$
∴ the points of discontinuity are
$x=1, x=-1$ and $x=-3$ only.

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