# How do you find the domain and range of sqrt(x^2 - 9)?

Jul 4, 2017

Domain = $x$
Range = $x \ge 3$
The domain is just the input, the variable=s) being changed. In thus case it is just $x$.
The range is the set of values of $x$ which can plotted onto a graph. The lowest possible value for $y$ is 0. So, $0 = \sqrt{{x}^{2} - 9}$, $0 = {x}^{2} - 9$, $9 = {x}^{2}$, $x = \sqrt{9} = 3$. $\sqrt{{3}^{2} - 9} = \sqrt{9 - 9} = \sqrt{0} = 0$.