Number of elements in the range of the function is: (Where is the greatest integer function)

JEE MainMathematicsModerateITF

Number of elements in the range of the function
$\ f(x) = \tan^{- 1}\sqrt{\lbrack x\rbrack + \lbrack - x\rbrack} + \sqrt{2 - |x|} + \frac{1}{x^{2}}$
is:
(Where is the greatest integer function)

Show answer and solution

Domain

2 - |x| \geq 0

\Rightarrow |x| \leq 2

\Rightarrow x = - 2, - 1,0,1,2

x = \pm 1

y = 2

x = \pm 2\

y = \frac{1}{4}

Source: Grass-G / M-17 Mathematics Paper 26 Nov Second.docx

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