A Question about the Domain and Range of a Function

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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?
 
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Answers and Replies

  • #2
Dick
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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,∞)??
 
  • #3
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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.
 
  • #4
Dick
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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.

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
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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.

Oh, I see, thank-you!
 

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