Is this statement about this continuous function correct? Is it true that if $f^2$ is continuous, then $\lvert f \rvert$ is continuous?
Can I say that since $f^2 \geq 0$ then $\lvert f \rvert = \sqrt{f^2}$ and that indicates that $\lvert f \rvert$ is also continuous beacuse of the arithmetic property of continuous functions?

Yes, the square root function is continuous in its domain, and composition of continuous functions is continuous.
