Functions Modeling Change: A Preparation for Calculus, 5th Edition

Assume that $g(x)$ can equal zero for some $x$. This means that $g(x)=0$, or $$0=\frac{3}{\sqrt{x^2+4}}$$ There doesn't exist a number that can divide $3$ into zero, however. Thus, $g(x)$ can never be zero. The statement is true.