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Is this function injective and surjective?

Let $f(x)=x^2$. In each of the following cases, is this function injective and/or surjective?

  1. $f: \mathbb{R} \longrightarrow [0,\infty)$, I know this is surjective but not injective.

  2. $f: \mathbb{C} \longrightarrow \mathbb{C}$. 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.

  3. $f: \mathbb{R} \longrightarrow \mathbb{R}$. This is neither surjective nor injective.

  4. $f: \mathbb{R} \cup \{x \in \mathbb{C} : \mathrm{Re}(x) = 0\} \longrightarrow \mathbb{R}$. I dont really know how to deal with complex function definitions.

  5. $f: \{z=x+iy: i^2=-1, y>0\} \cup \{z=x+iy: i^2=-1, y=0 \text{ and } x \ge 0\} \longrightarrow \mathbb{C}$..

Thanks a lot. I do know what surjective and bijective means, but I don't know how to prove it over complex subsets.

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    Better to edit your original question than to repost it. Better yet to accept some answers to your other questions. Please see http://meta.math.stackexchange.com/questions/3399/why-should-we-accept-answers2012-08-18

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