The range of sin-1x2+12+cos-1x2-12, where [.] denotes the greatest integer function, is

x2+12=x2-12+1=1+x2-12.Thus, from domain point of view,x2-12=0,-1  or  x2+12=1,0i.e.,fx=sin-11+cos-10   or  sin-10+cos-1-1or    fx=π