Q:

f and g are bounded . if 1/g is bounded, then f/g is bounded.

I would like some help understanding how to go about this question. I think that f/g is not bounded, but I cannot figure how to show that f/g is not bounded.

A:

We have $|f| < P$, $|g| < Q$, and $|1/g| < R$ for some $P$, $Q$, and $R$, so
$$\left|\frac{f}{g} \right|= \left| f\frac{1}{g} \right| < PR.$$

