Q123 / 200 · Manipal (MET) 2014 · Mathematics

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

  • A
    all $x$
  • B
    no $x$
  • Correct answer
    C
    all integral points
  • D
    $x$ which is not an integer

Solution

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

Hence, the correct answer is option: 'C'.

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