Consider the function $g$:$RR$ given by

$g(x)=|$~$x$~$|-x$

$($a$)$ Is there an element $a$ in the domain that satisfies $g(a)=0\mathrm{.}5?$ If you think there is write down such an element and

explain why it works. If you think there is not, explain why not.

$($b$)$ Is there an element $a$ in the domain that satisfies $g(a)=1\mathrm{.}5?$ If you think there is write down such an element and

explain why it works. If you think there is not, explain why not.

$($c$)$ Which, if any, inputs ainR result in the output $g(a)=0?$