The number of points at which the function $f(x) =\frac{1}{\log|x|}$ is discontinuous is
Answer & explanation
Correct answer: option 3
The function log |x| is not defined at x = 0, and hence x = 0 is a point of discontinuity.
Also, for f(x) to be defined, log|x| ≠ 0 that is x ≠ ±1.
Hence, 1 and –1 are also points of discontinuity.
Clearly f(x) is continuous for x ∈ R – {0, 1, –1}.
Thus, there are three points of discontinuity.
Hence (C) is the correct answer.