Period of `f(x) = sgn([x] +[-x])`is equal to (where [.] denotes greatest integer function

The value of int_(-1)^(10)sgn(x-[x])dx is equal to (where,[:] denotes the greatest integer function

If f(x) = [x] - [x/4], x in R where [x] denotes the greatest integer function, then

The period of the function f(x)=sin(x+3-[x+3]) where [] denotes the greatest integer function

int_(-10)^(0)(1(2[x])/(3x-[x])/(2[x])/(3x-[x]))dx is equal to (where [*] denotes greatest integer function.) is equal to (where [*] denotes greatest integer function.)

If f(x)=[2x], where [.] denotes the greatest integer function,then

The domain of f(x)=log_([x])[x]+log_({x}){x} (where I.] denotes greatest integer function and ( denotes fractional function) is

The range of the function f(x)=sgn(x-[x])+1 is (where [.] is the greatest integer function)

Let f(x)=(-1)^([x]) where [.] denotes the greatest integer function),then

The function f(x)=[x^(2)]+[-x]^(2) , where [.] denotes the greatest integer function, is