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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY1 Mark
Question
Choose the correct answers from the given four options:
The function $\text{f(x)}=\frac{4-\text{x}^2}{4\text{x}-\text{x}^3}$ is:
  1. Discontinuous at only one point.
  2. Discontinuous at exactly two points.
  3. Discontinuous at exactly three points.
  4. None of these.
✓

Answer

  1. Discontinuous at exactly three points.

Solution:

We have, $\text{f(x)}=\frac{4-\text{x}^2}{4\text{x}-\text{x}^3}=\frac{(4-\text{x}^2)}{\text{x}(4-\text{x}^2)}$

$=\frac{(4-\text{x}^2)}{\text{x}(2^2-\text{x}^2)}=\frac{4-\text{x}^2}{\text{x}(2+\text{x})(2-\text{x})}$

Clearly, f(x) is discontinuous at exactly three points x = 0, x = -2 and x = 2.

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