Finding the Domain of an Algebraic Function

[NelsonsXanadu]

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

 

[Mark44]

Homework Statement

Find the Domain

f(x) = ___2___
x+3

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

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?

 

[NelsonsXanadu]

Well a -3 would make the denominator 0...

 

[Mark44]

So -3 is not in the domain. Are there any other values for which this function is undefined?

 

[cyby]

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.