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$The number of elements in the domain of the function$ $f (x) = \sin^{- 1} (\frac{x^{2} - 2 x}{3}) + \sqrt{[x] + [- x]}, (where [.] denotes$ $the greatest integer function) is equal to$

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Correct option is D

f(x)=sin−1⁡x2−2x3+[x]+[−x]sin−1⁡x2−2x3 is defined for −1≤x2−2x3≤1 and [x]−[−x] is defined only for integral values of x⇒ x=−1,0,1,2,3

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The number of elements in the domain of the function f(x)=sin−1⁡x2−2x3+[x]+[−x], (where [.] denotes the greatest integer function) is equal to

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$The number of elements in the domain of the function$ $f (x) = \sin^{- 1} (\frac{x^{2} - 2 x}{3}) + \sqrt{[x] + [- x]}, (where [.] denotes$ $the greatest integer function) is equal to$