JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The real valued function \(f(x)=\frac{\operatorname{cosec}^{-1} x}{\sqrt{x-[x]}, \text { where }}\) \([ x ]\) denotes the greatest integer less than or equal to \(x,\) is defined for all \(x\) belonging to
- A all reals except integers
- B all non-integers except the interval \([-1,1]\)
- C all integers except \(0,-1,1\)
- D all reals except the Interval \([-1,1]\)
Answer & Solution
Correct Answer
(B) all non-integers except the interval \([-1,1]\)
Step-by-step Solution
Detailed explanation
\(f( x )=\frac{\operatorname{cosec}^{-1} x }{\sqrt{\{ x \}}}\) Domain \(\in(-\infty,-1] \cup[1, \infty)\) \(\{ x \} \neq 0\) so \(x \neq\) integers
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