Question

The set of points of discontinuity of $f\left(x\right)=\frac{1}{x-\left[x\right]}$ is ________.

Answer 1

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

x – [x] = 0

⇒ x = [x]

⇒ 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 $f\left(x\right)=\frac{1}{x-\left[x\right]}$ is the set of integers i.e. Z.


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