First slide

Continuity

Question

The function $f (x) = \frac{4 - x^{2}}{4 x - x^{3}}$ is

Moderate

A

discontinuous at only one point
B

discontinuous exactly at two points
C

discontinuous exactly at three points
D

none of these

Solution

$\begin{array}{l} We have f (x) = \frac{4 - x^{2}}{4 x - x^{3}} \\ Clearly, there are three points of discontinuity, viz ., 0, 2, - 2 \end{array}$

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