Finding the Domain of an Algebraic Function

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Homework Help Overview

The discussion revolves around finding the domain of the algebraic function f(x) = 2/(x + 3). Participants are exploring the conditions under which the function is defined, particularly focusing on the implications of division by zero.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to identify the values of x that would make the denominator zero, questioning whether the domain includes all numbers except zero or if other values should be considered.

Discussion Status

The discussion is actively exploring the implications of the denominator being zero, with participants clarifying that -3 is not in the domain. There is an ongoing examination of whether there are additional values that might render the function undefined.

Contextual Notes

Participants are discussing the constraints of the function's domain, specifically focusing on the condition that the denominator cannot equal zero. The original poster's initial assumption about zero being excluded from the domain is being questioned and clarified.

NelsonsXanadu
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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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