Given `f(x)=[log_a (a|[x]+[-x]|)^x((a^((2/(([x]+[-x])))/(|x|)-5))/(3+a^(1/(|x|)))` for `|x| !=0 ; a lt 1 and 0 for x=0` where [ ] represents the integral part function, then

If f(x)={x^(2{e^((1)/(x))}),x!=0k,x=0 is continuous at x=0, where {^(*)} represents fractional part function,then

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

f:(2,3)->(0,1) defined by f(x)=x-[x] ,where [dot] represents the greatest integer function.

Given f(x)={3-[cot^(-1)((2x^3-3)/(x^2))] for x >0 and {x^2}cos(e^(1/x)) for x<0 (where {} and [] denotes the fractional part and the integral part functions respectively). Then which of the following statements do/does not hold good?

If f(x)= {(|1-4x^2|,; 0 lt= x lt 1), ([x^2-2x],; 1 lt= x lt 2):} , where [.] denotes the greatest integer function, then f(x) is

Given a real valued function f such that f(x)={tan^2[x]/(x^2-[x]^2) , x lt 0 and 1 , x=0 and sqrt({x}cot{x}) , x lt 0 where [.] represents greatest integer function then

Given f(x)={{:(3-[cot^(-1)((2x^3-3)/(x^2))], x >0) ,({x^2}cos(e^(1/x)) , x<0):} (where {} and [] denotes the fractional part and the integral part functions respectively). Then which of the following statements do/does not hold good?

Let g(x) = x - [x] - 1 and f(x) = {{:(-1", " x lt 0),(0", "x =0),(1", " x gt 0):} [.] represents the greatest integer function then for all x, f(g(x)) = .

Let g(x) = x - [x] - 1 and f(x) = {{:(-1", " x lt 0),(0", "x =0),(1", " x gt 0):} [.] represents the greatest integer function then for all x, f(g(x)) = .