`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 inverse of the function: f:(2,3) to (0,1) defined by f(x)=x-[x], where[.] represents the greatest integer function

lim_(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the greatest integer function). (a)-1 (b) 1 (c) 0 (d) does not exist

Statement 1: f(x)=cos x is continous at x=0a n dg(x)=[tanx],"w h e r e"[dot] represents greatest integer function, is discontinuous at x=0,t h e nh(x)=f(x)dotg(x) is discontinuous at x=0. Statement 2: If f(x) is continous and g(x) is discontinuous at x=a ,t h e nh(x)=f(x)g(x) is discontinuous at x=a

Evaluate: int_(-100)^(100)[tan^(-1)x]dx ,w h e r e[x] represents greatest integer function.

The domain of f(x)=ln(a x^3+(a+b)x^2+(b+c)x+c), where a >0,b^2-4a c=0,i s(w h e r e[dot] represents greatest integer function).

Evaluate: int_(0)^(oo)[2e^(-x)]dx, where [x] represents greatest integer function.

If p=(8+3sqrt(7))^n a n df=p-[p],w h e r e[dot] denotes the greatest integer function, then the value of p(1-f) is equal to a.1 b. 2 c. 2^n d. 2^(2n)

If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represent the greatest integer function)

lim_(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greatest integer function )

Find the domain of the function f(x)=log_(e)(x-[x]) , where [.] denotes the greatest integer function.