The function 'g' defined by gx=sinsin-1x+cossin-1x-1 where {x} denotes the functional part function is

gx=sinsin-1x+cossin-1x-1           =x+coscos-11-x-1           =x+1-x-1If   x∈  I   then    x=0    then   gx=0If  x∉I   then  -x=1-x⇒    g-x=1-x+x-1=gx⇒    g-x=gx⇒    gx  is  even   function.Also   gx   is   periodic  function