Consider the function g given by $g(x)=|x-4|+3.$

$($a$)$ For what $x-$value$($s$)$ is the function not differentiable?

$($b$)$ Evaluate $g^{\text{'}}(0),g^{\text{'}}(1),g^{\text{'}}(7),$ and $g^{\text{'}}(12).$

$($a$)$ The function is not differentiable at $x=$