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Q.
The number of points at which the function $f(x) = \frac{1}{\log |x|}$ is discontinuous is
Continuity and Differentiability
Solution:
The function log | x | is not defined at x = 0
so, x = 0 is a point of discontinuity.
Also, for f (x) to defined, log | x | = 0 that is $x \neq \pm 1$
.
Hence 1 and -1 are also points of discontinuity. Clearly $f (x)$ is continuous for $x \in R - \{0, 1, -1\}$.
Thus there are three points of discontinuity.