# A Question about the Domain and Range of a Function

1. Sep 28, 2013

### student34

1. The problem statement, all variables and given/known data

I constructed my own question to try to make sense of the following notation.

g(x) = 2√x g : X → Y. What does X and Y equal?

2. Relevant equations

For 2√x, x = or > than 0.

3. The attempt at a solution

g(x) = 2√x g : [0, ∞) → [0, ∞)

So X = Y = [0, ∞)

The reason why I am doing this is because my book shows this: g(x) = 2√x g : [1,∞) → [2,∞). Why does my book have a 1 instead of a 0 as an initial x value?

Last edited: Sep 28, 2013
2. Sep 28, 2013

### Dick

You have found the LARGEST domain that that function can be defined on. X could always be defined to be a subset of that domain, in which case your job is to figure out the corresponding Y. Are you sure the book didn't tell you X=[1,∞)??

3. Sep 28, 2013

### student34

The book just shows this, "g(x) = 2√x g : [1,∞) → [2,∞)" as an example of, "g : B → C". I just used X and Y for this thread.

4. Sep 28, 2013

### Dick

The book could also have said correctly that "g(x) = 2√x g : [4,∞) → [4,∞)". That would work also, right? Nothing in the problem really fixes what X HAS to be.

5. Sep 29, 2013

### student34

Oh, I see, thank-you!