If `f` is the greatest integer function and `g` is the modulus function, then find the value of `(gof)(-5/3)-(fog)(-5/3)dot`

The greatest integer function f(x)=[x] is -

If the function f(x)=[((x-2)^3)/a]sin(x-2)+acos(x-2),[dot] denotes the greatest integer function, is continuous in [4,6], then find the values of adot

In the questions, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. If y=3[x]+1=4[x-1]-10 , then find the value of [x+2y]dot

If [dot] denotes the greatest integer function, then find the value of lim_(x->0) ([x]+[2x]++[n x])/(n^2)

If f(x)=2|x|-3[x] where [x] denotes greatest integer in x not exceeding the value of x, find the value of f(2.5) and f(-2.5).

If f(x) is an even function and satisfies the relation x^2dotf(x)-2f(1/x)=g(x),w h e r eg(x) is an odd function, then find the value of f(5)dot

If the function f(x)=[3.5 + b sin x] (where[.] denotes the greatest integer function) is an even function then complete set of values of 'b' is :

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

f(x)=(cosx)/([(2x)/pi]+1/2), where x is not an integral multiple of pi and [dot] denotes the greatest integer function, is an odd function an even function neither odd nor even none of these

Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3] , where [*] represents the greatest integer function and {*} represents the fractional part of x. Draw the graph of y= f(x) . Prove that y=f(x) is bijective. Also find the range of the function.