The function $\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi$, where $[\cdot]$ denotes the…
The function $\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi$, where $[\cdot]$ denotes the greatest integer function, is discontinuous at
(A) all irrational numbers $x$.
no $x$.
all integer points.
every rational $x$ which is not an integer.
Solution
Greatest integer function is discontinuous on integer values.
$\therefore \quad \mathrm{f}(x)$ is discontinuous at all integer points.