Textbook Problem

Prove Theorem 11.2.7(b): If f and g are real-valued functions defined on the same set of nonnegative integers and if $f\left(n\right)\ge 0$ and $g\left(n\right)\ge 0$ for every integer $n\ge r$. where r is a positive real number, then if $f\left(n\right)$ is $\Theta \left(g\left(n\right)\right)$ . then $g\left(n\right)$ is $\Theta \left(f\left(n\right)\right)$ .