# Is this function injective and surjective?

Let $f(x)=x^2$. Is this function injective and surjective if the function is defined as:

1. $f: \mathbb{R} \longrightarrow [0,\infty)$.

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

3. $f: \mathbb{R} \longrightarrow \mathbb{R}$.

4. $f: \mathbb{R} \cup \{x \in \mathbb{C} : \mathrm{Re}(x) = 0\} \longrightarrow \mathbb{R}$.

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!

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Please, consider learning to write in TeX. –  Sigur Aug 17 '12 at 1:06
$f:\mathbb{R}\to[0,\infty)$, $x\mapsto x^2$ is not 1-1 since $f(-1)=f(1)=1$. –  Sigur Aug 17 '12 at 1:07
Can you not do any part of this? Do you know what injective means? What surjective means? It's best if you show us what you can do and where you get stuck, so we know where to start giving help. –  Gerry Myerson Aug 17 '12 at 1:46