Answer
Domain: all the real numbers such that $x\leq3$
The zero:
$x=-97$
Work Step by Step
$f(x)=10-\sqrt {3-x}$
Domain:
$3-x\geq0$
$-x\geq-3$
$x\leq3$
The zeros:
$f(x)=0$
$10-\sqrt {3-x}=0$
$10=\sqrt {3-x}~~$ (Square both sides)
$100=3-x$
$x=3-100$
$x=-97$
Check the zero:
$10-\sqrt {3-x}=10-\sqrt {3-(-97)}=10-10=0$
