How to find the domain in one dimension

[tomfrank]

Homework Statement

I am trying to find the domain of the following..

R^2 to R^3 of g(x,y) = (x-y,x+y,3*x)
R^3 to R of h(x,y,z) = x/(y+z)

Homework Equations

The Attempt at a Solution

I don't know how to start. I know how to find the domain in one dimension but how do you do it in 2 or 3 dimensions?
Thanks

 

[Dick]

Your second function is actually R^3->R. Since they didn't tell you what the domain is, you just want to pick the domain of f:A->B to be all of the points in A where the function is defined.

 

[tomfrank]

so for the first one can just do from (-infinity to infinity) ?

can i just put in any value of x i want to?

 

[Mark44]

For the first one, your domain is not just R, the real line; it's the real plane, R². For the second one, there is a restriction on y and z.

 

[Dick]

so for the first one can just do from (-infinity to infinity) ?

can i just put in any value of x i want to?

Basically, yes. But the domain isn't (-infinity,infinity), that's a subset of R. The domain should be a subset of R^2. How about saying it's ALL of R^2?

 

[tomfrank]

So the first one domain = R^2 the real plane

second one = is y+z not equal to '0'

is that right?

 

[Mark44]

Yes, pretty much. You can say it a little nicer as
$$\{(x, y, z)\in R^3 | y + z \neq 0\}$$.

 

[tomfrank]

that looks nice thanks