question about the convergence of a function

Question

I'll start off with what I know:

I know that if I have two functions f(x) and g(x)

if: $$ \int_0^\infty f(x) < \int_0^\infty g(x) $$

If g(x) converges as the values function approaches infinity, I know that f(x) also converges.

Here's my question:

If f(x) < g(x), and f(x) does not converge, does that mean that g(x) also does not converge?

Answer 1

If $f(x)$ converges, you don't know anything about $g(x)$ If $f(x)$ diverges, then certainly $g(x)$ diverges