Choose any e > 0 ==> there exists a real number M s.t. |f(x) - L| < e whenever x > R.
Since g(x) --> oo when x --> oo there exists a number T s.t. g(x) > R whenever x > T ==> for ANY x > T you get
|f(g(x)) - L| < e , and this means f(g(x)) --> L when x --> oo
Tonio