Q49 / 90 · JEE Main 2012 (Offline) · Mathematics

If $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ is a function defined by $f(x)=[\mathrm{x}] \cos \left(\frac{2 x-1}{2}\right) \pi$, where $[\mathrm{x}]$ denotes the greatest integer function, then $f$ is

  • Correct answer
    A
    continuous for every real $x$
  • B
    discontinuous only at $x=0$
  • C
    discontinuous only at non-zero integral values of $x$
  • D
    continuous only at $x=0$

Solution

$f(x)=[x] \cos \left(\frac{2 x-1}{2}\right) \pi=[x] \cos \left(x-\frac{1}{2}\right) \pi$ $=[x] \sin \pi x$ is continuous for every real $x$.

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

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