Linear Independence and Linear Dependence of "x" and "abs(x)"

Question

I would like to understand why the $f_1=x$ and $f_2=|x|$ are linear independence functions. Could someone explain me?. As I see they are not independece function due

$c_1f_1+c_2f_2=0$

if $c_1=1$ and $c_2=-1$, we have

$x-|x|=0$

Thanks for you help

Answer 1

So as they are not equal to zero for all x in $(-\infty,\infty)$ we could conclude they are linear independence?