Choose the correct answers from the given four options : The func… - Vidyadip

MCQ

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 :

A
Discontinuous at only one point.
B
Discontinuous at exactly two points.
✓
Discontinuous at exactly three points.
D
None of these.

✓

Answer

Correct option: C.

Discontinuous at exactly three points.

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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