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

Given that f(x)=sin−1⁡x2−2x3+[x]+[−x] Now, [x]+[−x] is defined only for integral values of ' x '    And sin−1⁡x2−2x3 is defined when −1≤x2−2x3≤1 If x2−2x3≥−1⇒x2−2x+3≥0D<0 It has no real values and  ifx2−2x3≤1⇒x2−2x−3≤0⇒(x+1)(x−3)≤0⇒x∈[−1,3]∴ Domain of f(x) is [−1,3]∴x∈{−1,0,1,2,3} (∵ Integralvalues only )∴ Number of integral elements in the domain are 5