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JEE Main 2012Offline
Exam
JEE Main
Year
2012
Mode
Offline
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2012 · Offline · Mathematics · Continuity and Differentiability

If f: R arrow R is a function defined by f(x)=[x] ((2 x-1)/(2)) π ,...

If f:R→R\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R} is a function defined by f(x)=[x]cos⁡(2x−12)πf(x)=[\mathrm{x}] \cos \left(\frac{2 x-1}{2}\right) \pi, where [x][\mathrm{x}] denotes the greatest integer function, then ff is

Options

  1. Acontinuous for every real xx
  2. Bdiscontinuous only at x=0x=0
  3. Cdiscontinuous only at non-zero integral values of xx
  4. Dcontinuous only at x=0x=0

Correct answer

A. continuous for every real xx

Step-by-step solution

f(x)=[x]cos⁡(2x−12)π=[x]cos⁡(x−12)πf(x)=[x] \cos \left(\frac{2 x-1}{2}\right) \pi=[x] \cos \left(x-\frac{1}{2}\right) \pi =[x]sin⁡πx=[x] \sin \pi x is continuous for every real xx.
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