Answer
$[10,\infty)$
Work Step by Step
We are given the function:
$f(x)=\dfrac{x+2}{\sqrt{x-10}}$
There are two conditions we must set:
1) the radical must make sense
2) the denominator is not zero
For the first condition to be met we solve:
$x-10\geq 0$
$x\geq 10$
For the second condition to be met we solve:
$\sqrt{x-10}\not=0$
$x-10\not=0$
$x\not=0$
Therefore using both conditions we get the domain of $f$:
$x\gt 10$
$(10,\infty)$
