Question

The number of points at which the function $f(x)=\frac{1}{\log |x|}$ is discontinuous is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

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 $x\ne \pm 1$
. 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.