Medium MCQ +4 / -1 PYQ · JEE Mains 2021

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 :

A all real except integers
B all non-integers except the interval [ $-$1, 1 ] Correct answer
C all integers except 0, $-$1, 1
D all real except the interval [ $-$1, 1 ]

Solution

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 = $( - \infty , - 1] \cup [1,\infty ) - I$

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Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations

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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 :

Solution

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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 :