\text { Let } f \text { be a continuous function on }(0, \infty) \text { such that } \lim _{x \rightarrow 0^{+}} f(x)=\infty \text { and } \text {

If } \int_{2}^{\infty} g(x) d x \text { converges, then } \int_{2}^{\infty} f(x) d x \text { converges. } \int_{2}^{\infty} f(x) d x \text { converges. } \text { If } \int_{2}^{\infty} f(x) d x \text { converges, then } \int_{2}^{\infty} g(x) d x \text { converges. } \text { If } \int_{2}^{\infty} g(x) d x \text { diverges, then } \int_{2}^{\infty} f(x) d x \text { diverges. } \int_{2}^{\infty} f(x) d x \text { diverges. }