The set of points of discontinuity

Question:

The set of points of discontinuity of $f(x)=\frac{1}{x-[x]}$ is______________

Solution:

The function $f(x)=\frac{1}{x-[x]}$ is discontinuous when $x-[x]=0$.

$x-[x]=0$

$\Rightarrow x=[x]$

$\Rightarrow x$ is an integer

So, the function f(x) is discontinuous for all x ∈ i.e. the set of integers.

Thus, the set of points of discontinuity of $f(x)=\frac{1}{x-[x]}$ is the set of integers i.e. $\mathbf{Z}$.

The set of points of discontinuity of $f(x)=\frac{1}{x-[x]}$ is the set of integers i.e. Z

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