## Algebra and Trigonometry 10th Edition

$[10,\infty)$
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 $f$: $x\gt 10$ $(10,\infty)$