The true set of real values of `x` for which the function `f(x)=xlnx-x+1` is positive is

The true set of real values of x for which the function f(x)=x ln x-x+1 is positive is

The true set of real values of x for which the function, f(x) = x ln x – x + 1 is positive is

All possible value of x for which the function f(x)=x In x-x+1 is positive is

The largest set of real values of x for which ln(1+x)<=x is

The set of values of x for which the function f(x) = log ( (x - 1)/(x + 2) ) is continous , is

The set of real values of x for which f(x)=(x)/(Logx) is increasing is

The set of real values of x for which f(x)=(x)/(logx) is increasing is :

If [x] represent greatest interger lexand[alpha,beta] is the set of all real values of x for which the real function f(x)=(sqrt(3+x)+sqrt(3-x))/(sqrt([x]+2)) is defined then f^(2)(alpha+1)+5f^(2)(beta)=