Question 1060082
( x – 5 )^1/2 is the same as sqrt(x-5)


sqrt is shorthand for "square root"


With square roots, we cannot have the stuff inside be negative


x-5 cannot be negative. So force it to be either 0 or a positive value. I.e,


{{{x-5 >= 0}}}


isolate x and we get


{{{x >= 5}}}


Which is the domain. It's the set of allowed x values we can plug in. We can plug in 5 for x or any number that is larger than 5. 


The domain in set builder notation would look like this 
*[Tex \LARGE \left\{x|x\in\mathbb{R}, \ x \ge 5\right\}]


In interval notation, the domain is written like this <img src="http://www.sciweavers.org/tex2img.php?eq=%5B5%2C%20%5Cinfty%29&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="[5, \infty)" width="54" height="18" />