Verified Solution • 2025–26 Session moderate

QJEEM21Mac082: JEE Main 2021 Mathematics - Class 11 JEEM21Mac082 Solution: The real valued function f ( x ) = cos ⁡ e c − 1 x x − [ x ] ,…

The real valued function
f(x)=cos⁡ec−1xx−[x], where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :

Multiple Choice Options

  • A all real except integers
  • B all non-integers except the interval [ −1, 1 ]
  • C all integers except 0, −1, 1
  • D all real except the interval [ −1, 1 ]

Step-by-Step Verified Solution

Domain of cos⁡ec−1x :

x∈(−∞,−1]∪[1,∞)

and, x−[x]>0

⇒{x}>0

⇒x≠I

∴ Required domain = (−∞,−1]∪[1,∞)−I

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