Question

Consider the following statements:
$1.f\left(x\right)=\left[x\right]$, where $[.]$ is the greatest integer function, is discontinuous at $x=n$, where $nϵZ$.
$2.f\left(x\right)=\cos x$ is discontinuous at $x=n\pi$, where $nϵZ$.
Which of the above statements is/are correct?

• A. $1$ only
• B. $2$ only
• C. Both $1$ and $2$
• D. Neither $1$ nor $2$

Answer 1

Answer: (A)

$1$ only

The greatest integer function is discontinuous at all the integers .

But $\cos x$ is a continuous function throughout .

Thus, only Statement 1 is correct.