The number of elements in the domain of the function `f(x)=sin^(-1)((x^2-2x)/3)+sqrt(([x]+[-x]))` , (where [.] denotes the greater integer function) is equal to a. 4 b. 6 c. 3 d. 5

Options

A. 6
B. 4
C. 3
D. 5

Answer

D

Explanation

`f(x)=sin^(-1)((x^(2)-2x)/(3))+sqrt([x]+[-x])`
`sin^(-1)((x^(2)-2x)/(3))"is denfined for"-1le(x^(2)-2x)/(3)le1`
and `sqrt([x]-[-x])` is defined only for integral values of x
`rArr" "x=-1,0,1,2,3`