# Questions Regarding Definition of One-to-One and Onto Functions?

1. Oct 20, 2012

Hi, I was just having a little trouble of understanding what it... is saying, well first I'll state what my book says the definition is:

A function T:D* $\subseteq$ R2 → R2 is called one-to-one if for each (u,v) and (u',v') in D*, T(u,v)=T(u',v') implies that u = u' and v = v'

A function T:D* $\subseteq$ R2 → R2 is called onto D if for every point (x,y) $\in$ D there is a point (u,v) in D* such that T(u,v) = (x,y)

So just a couple of questions (they might be stupid... sorry):

1. Now correct me if I'm wrong but the function T, is supposed to bring a domain in D* to D right? So isn't there a problem that there are two points, (u,v), and (u',v') that goes to the same point?

2. Isn't the definition for a function to be onto, is a definition for all functions? Because that's what a function does right? f(x) = y, you put x in, and it gives you "y"

2. Oct 20, 2012

### DonAntonio

No, there is no problem...but THAT function won't be 1-1 then
No. For example, the function $\,f:\Bbb R\to\Bbb R\,\,\,,\,\,f(x)=x^2\,$ isn't onto as no negative number is the square or no real number.

DonAntonio

3. Oct 20, 2012