Range of the function f(x) = Sin^-1[x^2+1/2] + cos^-1[x^2-1/2] where [] is the greteast integer function is??? I need the procedure

first of all the domain should be defined

clearly x² -1/2 should be less than 2 (as the bracket gives the integer only)

we get the domain as -root(3/2) to + root(3/2)

put the extremes and get the answer....