The range of the function f x = s i n - 1 x 2 - 1 3 - c o s - 1 x 2 + 2 3 is (where, x represents the greatest integer value of x )

Step-by-step solution

x 2 - 1 3 = x 2 + 2 3 - 1 = x 2 + 2 3 - 1 = k   let Now, the function is s i n - 1 k - c o s - 1 k + 1 For the above function to be defined, - 1 ≤ k ≤ 1   &   - 1 ≤ k + 1 ≤ 1 ∴ k = - 1,0 ∴ Range = s i n - 1 - 1 - c o s - 1 0 , s i n - 1 0 - c o s - 1 1 = - π , 0