TITLE: PreCalculus Domain of a function
QUESTION [0 upvotes]: What is the domain of $(x-3)^{1/2}\;?$
The domain would be $x>3$ wouldn't it? Because the graph doesn't exist until after the point $(3,0)$

REPLY [0 votes]: $\sqrt{x-3}$ is defined (on the real line) only for $x-3\geqslant0 \iff x\geqslant3$, so $$\rm{dom}(f)=[3,\infty).$$
(Also, remember that infinity is not a real number, so we have to exclude it from our interval).
So, you're almost right. It's just that you have to include $3$ in your domain, since $\sqrt{3-3}=0 \in \mathbb{R}$ is well-defined in the reals.
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