Chapter 2 - Functions - 2.2 Domain and Range - Exercises and Problems for Section 2.2 - Exercises and Problems - Page 82: 21

$\textbf{Domain: }\quad x > 4 $ $\textbf{Range:}\quad y >0$

The denominator of the function can not be zero and must be positive because of the square root : $f(x)=\frac{1}{\sqrt{x-4}}.$ So $x=4$ must be excluded from the domain of the function. The domain is $x>4$ and the range is $y>0$.