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  4. The number of points at which the function f ( x )=(1/ x -[ x ]),[.] denotes the greatest integer function is not continuous is

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Q. The number of points at which the function $f ( x )=\frac{1}{ x -[ x ]},[.]$ denotes the greatest integer function is not continuous is

Continuity and Differentiability

Solution:

$x-[x]=0$ when $x$ is an integer, so that $f(x)$ is discontinuous for all $x \in$ I i.e., $f ( x )$ is discontinuous at infinite number of points.