JEE Main202118 Mar 2021Morning ShiftMathematicsFunctionsActual

The real valued function f x = cosec - 1 x x - [ x ] , where x denotes the greatest integer less than or equal to x , is defined for all x belonging to:

Options

Aall reals except integers
Ball non-integers except the interval   - 1 , 1
Call integers except 0 , - 1 , 1
Dall reals except the Interval - 1 , 1

Correct answer

B. all non-integers except the interval   - 1 , 1

Step-by-step solution

Given f x = cosec - 1 x x Domain of cosec - 1 x ∈ ( - ∞ , - 1 ] ∪ [ 1 , ∞ ) We know, x ≠ 0 , so x ≠ integers. So, x belongs to all non-integers except the interval - 1 , 1 .  

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