Find the range of `f(x)=(x-[x])/(1-[x]+x '),w h e r e[]` represents the greatest integer function.

Find the points of discontinuity of the function: f(x)=[[x]]-[x-1],w h e r e[dot] represents the greatest integer function

Discuss the differentiability of f(x)=[x]+|1-x|, x in (-1,3),w h e r e[dot] represents greatest integer function.

f:(2,3)vec(0,1)d efin e db yf(x)=x-[x],w h e r e[dot] represents the greatest integer function.

Find the domain of f(x)=sqrt(([x]-1))+sqrt((4-[x])) (where [ ] represents the greatest integer function).

Draw the graph of f(x)=[tan^(-1)x]," where "[*]" represents the greatest integer function".

Evaluate the following limits using sandwich theorem: lim_(x->oo)([x])/x ,w h e r e[dot] represents greatest integer function.

Find the period of the following. (i) f(x)=(2^(x))/(2^([x])) , where [.] represents the greatest integer function. (ii) f(x)=e^(sinx) (iii) f(x)=sin^(-1)(sin 3x) (iv) f(x) =sqrt(sinx) (v) f(x)=tan((pi)/(2)[x]), where [.] represents greatest integer function.

Find the domain and range of f(x)=sin^(-1)[x]w h e r[] represents the greatest function).

Evaluate: int_0^oo[2e^(-x)]dx ,w h e r e[x] represents greatest integer function.

If the domain of y=f(x)i s[-3,2], then find the domain of g(x)=f(|[x]|),w h e re[] denotes the greatest integer function.