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 ∈ Z 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