f(x) = (xsin(x) + cos(x) / 1 - cos(x)) + (|X| - 2 / x^2 -4)

f = (x Sin[x] + Cos[x]/1 - Cos[x]) + (Abs[x] - 2/x^2 - 4)
Plot[f, {x, -20, 20}]

Limit[f, x -> 0]
  (*-Infinity*)

   Limit[f, x -> Infinity]
   Limit[f, x -> -Infinity]

FunctionDomain[f, x]