The functionf(x) = [x] [ 2x - 1 2 ] , , where[.] denotes the grea… - Vidyadip

MCQ

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

A
All $x$
B
No $x$
✓
All integer points
D
$x$ which is not an integer

✓

Answer

Correct option: C.

All integer points

c
(c) $f(x) = [x]\cos \,\left[ {\frac{{2x - 1}}{2}} \right]\,\pi $

Since $g(x) = [x]$ is always discontinuous at all integral values of points.

Hence $f(x)$ is discontinuous for all integral points.

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