Answer
The domain is: $D=(1,4)$
Work Step by Step
We are give: $h(x)=\sqrt 4-x +\sqrt x^{2}-1$
We can't take the square root of a negative number, so:
$4-x\geq0$
$x\leq4$
$x^{2}-1\geq0$
$(x-1)(x+1)\geq0$
$x\leq-1$ or $x\geq1$
Therefore the domain is: $D=(1,4)$
