TITLE: What is the domain of this function
QUESTION [0 upvotes]: The domain of $f(x)= (x-1)^{1/2}$ are all the real numbers. Now I can sub in x=0 into the expression, and I get the square root of -1 which is a complex number. So is this okay?

REPLY [1 votes]: Assuming you are finding the domain over the real numbers ($\Bbb R$), then $$\sqrt {x-1} \geq 0$$
As you can't have the square root of a number less than 0 in the real numbers. Solve the expression by squaring it out and then putting the $1$ on the right hand side and you find the domain is:
All real $x$, where $x \geq 1$
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