Question

I know what the answer is just not how to exopress it. Can someone help me please?

State the domain of the function:

f(x)(2+x)/(3-x)

Now I know the domain is
(-infinity,3) U (3, infinity)?

(-infinity,3] U [3, infinity) ?
How do I express it? do I use ] brackets or open at the infinity and closed by the 3? i know x doesn't equal 3 so how do I show this in the answer? Thank you!

Answer 1

If you close at 3, then you are including 3, which will create division by zero in this case.

The variable x cannot be 3 for this rational function.

I'd say write it like this:

(-infinity,3) U (3, infinity)

The above interval notation is saying that x < 3 or x > 3.