JEE PYQ: Functions Question 3
Question 3 - 2021 (18 Mar Shift 1)
The real valued function $f(x) = \frac{\operatorname{cosec}^{-1} x}{\sqrt{x - [x]}}$, where $[x]$ denotes the greatest integer less than or equal to $x$, is defined for all $x$ belonging to:
(1) all reals except integers
(2) all non-integers except the interval [-1,1]
(3) all integers except 0, -1, 1
(4) all reals except the interval [-1,1]
Type: MCQ
Show Answer
Answer: (2) all non-integers except the interval [-1,1]
Solution
$f(x) = \frac{\operatorname{cosec}^{-1} x}{\sqrt{{x}}}$
Domain $\in (-\infty, -1] \cup [1, \infty)$
${x} \neq 0$ so $x \neq$ integers
BETA
