# A Question about the Domain and Range of a Function

## Homework Statement

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?

## Homework Equations

For 2√x, x = or > than 0.

## 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:

Dick
Homework Helper

## Homework Statement

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?

## Homework Equations

For 2√x, x = or > than 0.

## 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?

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,∞)??

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,∞)??

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.

Dick