Q. The function $f(x) = \lbrack x\rbrack\cos\left\lbrack \frac{2x - 1}{2} \right\rbrack\pi$ where [.] denotes the greatest integer function, is discontinuous at
A) All $x$
B) No $x$
C) All integer points
D) $x$ which is not an integer
Explanation
(c)
$f(x) = \lbrack x\rbrack\cos\left\lbrack \frac{2x - 1}{2} \right\rbrack\pi$
Since, $\lbrack x\rbrack$ is always discontinuous at all integer value, hence $f(x)$ is discontinuous for all integer value
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.