1. ## Define function

Hi everyone.
I've got a one task to do i need to show if the function g: R -> R^2 by g(x) = (x+1, x+2) is g onto?

I think is not but i do not really know how to show this understanding.
I'll be appreciate for any help.

Regards

2. Originally Posted by Snowboarder
Hi everyone.
I've got a one task to do i need to show if the function g: R -> R^2 by g(x) = (x+1, x+2) is g onto?
What number would map to $(0,0)?$

3. yes than it's not but how can i proof that mathematicly?

4. Originally Posted by Snowboarder
yes than it's not but how can i proof that mathematicly?
There is nothing to prove.
If $g(x)=(0,0)$ then $x+1=0~\&~x+2=0$.
What is wrong with that?

5. ok if you see the diagram you may better understand. the domain is a line. the codomain is a plain and the range is a straight line in that plane. now is that range line the same as full plane ?? how can that be ... this is a good way of illuminating things. keep track of pictures.

6. Simply assume that there exists $x \in {R}$ such that $g(x) = (0,0)$. This gives us:

(I) $x+1 = 0$
(II) $x+2 = 0$

$\Rightarrow x+1 = x+2 \Rightarrow 1 = 2 \Rightarrow$ contradiction.

So there is no $x \in {R}$ such that $g(x) = (0,0)$ and thus g is not onto