$|\mathcal{o}(f(x))| \leq \mathcal{o}(|f(x)|)$

Question

Let f(x) be a real continuous function

Is it true that $|\mathcal{o}(f(x))| \leq \mathcal{o}(|f(x)|)$

thanks.

P.S. $g(x)=\mathcal{o}(f(x))$ if $\lim \frac{g(x)}{f(x)}=0$