Answer
Domain: $[2,10)$
Work Step by Step
For a logarithmic function to be defined,
its argument must be POSITIVE.
Also, the square root function is defined
for non-negative arguments (may be zero).
So, h is defined when both terms are defined, or, for
$x-2\geq 0\qquad and\qquad 10-x>0$
$x\geq 2\qquad and\qquad 10>x$
So, for x greater or equal to 2, and less than 10.
Domain: $[2,10)$
