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:

Correct answer: B. all non-integers except the interval [- 1, 1] 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] .

JEE Main 202118 MarchMorning Shift

Exam: JEE Main
Year: 2021
Date: 18 March
Shift: Morning Shift
Subject: Mathematics
Chapter: Functions

JEE Main 2021 · 18 March · Morning Shift · Mathematics · Functions

The real valued function f (x) = cosec ^ - 1 x x - [ x ] , where...

The real valued function $f$ \left(x\right) = \dfrac{{cosec}^{- 1}x}{\sqrt{x - [ x ]}}, $where \left[x\right]$ 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 $\left[- 1, 1\right]$
Call integers except $0, - 1, 1$
Dall reals except the Interval $\left[- 1, 1\right]$

Correct answer

B. all non-integers except the interval $\left[- 1, 1\right]$

Step-by-step solution

Given $f\left(x\right) = \dfrac{{cosec}^{- 1}x}{\sqrt{{ x }}}$

Domain of ${cosec}^{- 1}x\in ( - \infty , - 1 ] \cup [ 1, \infty )$

We know, ${ x } \ne 0,$ so $x \ne$ integers.

So, $x$ belongs to all non-integers except the interval \left[- 1, 1\right] .

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