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

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of lim_(x to 0)(cosx)/(f(x)) is equal to where [.] denotes greatest integer function

The right hand derivative of f(x)=[x]t a npix at x=7 is (where [.] denotes the greatest integer function) a. 0 b. 7pi c. -7pi d. none of these

Period of f(x) = sin 3x cos[3x]-cos 3x sin [3x] (where[] denotes the greatest integer function), is

Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).

Draw the graph of f(x) = [x^(2)], x in [0, 2) , where [*] denotes the greatest integer function.

Number of points of discontinuity of f(x)=[sin^(-1)x]-[x] in its domain is equal to (where [.] denotes the greatest integer function) a. 0 b. 1 c. 2 d. 3

Draw the graph of y=[|x|] , where [.] denotes the greatest integer function.

Draw the graph of f(x)= [sqrtx], x in [0, 16) , where [*] denotes the greatest ineger function.

Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] denotes the greatest integer function, is

If f:R->R is defined by f(x)=[x−3]+|x−4| for x in R , then lim_(x->3) f(x) is equal to (where [.] represents the greatest integer function)