If $f$ has one root on $(-\infty,0)$ and two distinct roots on $(0,+\infty)$ and $f(0)=-1$, how many roots does $|f(|x|)|$ have?
I know graph of $|f(|x|)|$ should be in quadrant I because $x$ and $y$ have positive values only but I don't know what exactly happens to graph of $f$. Should it be symmetric with respect to the y-axis? So roots on $(-\infty,0)$ won't be roots? It'd have two distinct roots, Am I right?