Question

The function $f\left(x\right)=\left[x\right]\cos \left[\frac{2x-1}{2}\right]\pi$, where denotes the greatest integer function, discontinuous at

• A. All $x$
• B. No $x$
• C. All integral points
• D. $x$ which is not an integer

Answer 1

The correct option is C All integral points

We have $f\left(x\right)=\left[x\right]\cos \left[\frac{2x-1}{2}\right]\pi$
Since, $g\left(x\right)=\left[x\right]$ is always discontinuous at all integral values of points.

Hence, $f\left(x\right)$ is discontinuous for all integral points.