Possible Duplicates:
Reason why the even root of a number always positive
Square roots — positive and negative
I saw the following during a practice exam:
$f(x) = \sqrt x $ for $x ≥ 2$
After the exam, I pointed out to my teacher that this was not actually a function, but instead a mapping, because it can have both positive and negative values. She told me that this didn't matter; you assume the answer of $\sqrt x$ to be positive, unless otherwise stated. However, this contradicts her previous statement that $\sqrt x$ is a mapping. (She gave it as an example of something that was not a function, when defining functions.)
So, is $f(x)$ a function? Does it matter if there is a domain restriction?