Finding the Domain of an Algebraic Function

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The domain of the function f(x) = 2/(x + 3) is all real numbers except for -3, as this value makes the denominator zero and results in an undefined expression. The initial assumption that zero is excluded from the domain is incorrect; f(0) is defined and equals 2/3. The key point is to identify values that cause the denominator to be zero, which in this case is solely -3. Therefore, the correct domain can be expressed as all real numbers except -3. Understanding the function's behavior around its denominator is crucial for determining the domain accurately.
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Homework Statement



Find the Domain

f(x) = ___2___
x+3

Homework Equations





The Attempt at a Solution

I know this is a pretty simple question just want to make sure I'm on the right track. Wouldn't the domain be all numbers except zero? Because you can't divide by zero? How would I write this
 
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NelsonsXanadu said:

Homework Statement



Find the Domain

f(x) = ___2___
x+3
Another way to write this that is clearer is f(x) = 2/(x + 3)
NelsonsXanadu said:

The Attempt at a Solution

I know this is a pretty simple question just want to make sure I'm on the right track. Wouldn't the domain be all numbers except zero? Because you can't divide by zero? How would I write this
No, 0 is in the domain, because f(0) = 2/(0 + 3) = 2/3.
Yes, you cannot divide by zero. What value of x makes the denominator 0?
 
Well a -3 would make the denominator 0...
 
So -3 is not in the domain. Are there any other values for which this function is undefined?
 
What you are looking for is for the *denominator* to not be zero, such that you don't divide by zero. And you're right in saying that -3 is not in the domain. Just make sure that -3 is the only thing that's not in the domain.
 

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