For the given function $f(x)$ and numbers $L,c,$ and $>0,$ find the largest open interval about $c$ on which the inequality $|f(x)-L|<mi></mi>$ holds. Then give the largest value of $>0$ such that for all $x$ satisfying the inequality $|f(x)-L|<mi></mi>$ holds.

$f(x)=\sqrt[\phantom{2}]{12-x},L=2,c=8,=0\mathrm{.}1$

The largest open interval about $c$ on which the inequality $|f(x)-L|<mi></mi>$ holds is

$($Type integers or decimals.$)$

$$

$).$

Find the largest value $>0$ such that for all $x$ satisfying the inequality $|f(x)-L|<mi></mi><mi>r</mi>$ relds.

$=($Simplify your answer. Type an integer or a decimal.$)$