Possible Duplicate:
Is this function injective and surjective?
Let $f(x)=x^2$. In each of the following cases, is this function injective and/or surjective?
$f: \mathbb{R} \longrightarrow [0,\infty)$, I know this is surjective but not injective.
$f: \mathbb{C} \longrightarrow \mathbb{C}$. This one, I dont know how to see. I mean the function evaluated in the imaginary unity is -1, so I don't know how to deal with this.
$f: \mathbb{R} \longrightarrow \mathbb{R}$. This is neither surjective nor injective.
$f: \mathbb{R} \cup \{x \in \mathbb{C} : \mathrm{Re}(x) = 0\} \longrightarrow \mathbb{R}$. I dont really know how to deal with complex function definitions.
$f: \{z=x+iy: i^2=-1, y>0\} \cup \{z=x+iy: i^2=-1, y=0 \text{ and } x \ge 0\} \longrightarrow \mathbb{C}$..
Thanks a lot. I do know what surjective and bijective means, but I don't know how to prove it over complex subsets.