f[x_] = 1/x; g[x_] = Sqrt[x + 2];
F[x_] = f[g[x]];
Plot[F[x], {x, -2, 20}];

F[x] = 1/Sqrt[x + 2];
Domain = (-2, +Infinity);
Range = (0, +Infinity);

g[
          x_] = -x^4/(x^4 - 7  x^3 + 7  x^2 + 
              9);
glimit = 
        Limit[g[x], x -> -Infinity];
Print[glimit];

y[
          x_] = (x + x Cos[x])/(Sin[x] 
              Cos[x]);
Print[
        Limit[y[x], {x -> Infinity}]];

Plot[y[x], {x, 0, 10 Pi}]

Solution :  
      the limit is oscillating between  - 
        Infinity and  + Infinity.