JEE MAIN - Mathematics (2021 - 18th March Morning Shift - No. 10)
The real valued function
$$f(x) = {{\cos e{c^{ - 1}}x} \over {\sqrt {x - [x]} }}$$, where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :
$$f(x) = {{\cos e{c^{ - 1}}x} \over {\sqrt {x - [x]} }}$$, where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :
all real except integers
all non-integers except the interval [ $$-$$1, 1 ]
all integers except 0, $$-$$1, 1
all real except the interval [ $$-$$1, 1 ]
Explanation
Domain of $$\cos e{c^{ - 1}}x$$ :
$$x \in ( - \infty , - 1] \cup [1,\infty )$$
and, $$x - [x] > 0$$
$$ \Rightarrow \{ x\} > 0$$
$$ \Rightarrow x \ne I$$
$$ \therefore $$ Required domain = $$( - \infty , - 1] \cup [1,\infty ) - I$$
$$x \in ( - \infty , - 1] \cup [1,\infty )$$
and, $$x - [x] > 0$$
$$ \Rightarrow \{ x\} > 0$$
$$ \Rightarrow x \ne I$$
$$ \therefore $$ Required domain = $$( - \infty , - 1] \cup [1,\infty ) - I$$
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