Find the domain of f(x)=x³-43x²/√|x+9|

Question

suwhitney · Answer

I know that to find the domain you are only focusing on the denominator but when we were given the answer in class, we were told it was (-∞,-9)U(-9,∞) and im not really sure how he got that.

anonymous · Answer

You focus on the denominator because if the denominator becomes zero that is not legal in mathematics per se.

In your case there is a checkpoint as well, namely the$$\sqrt{\left| x+9 \right|}$$Now tell me, for what numbers does that become zero?

suwhitney · Answer

-9

anonymous · Answer

Great, so that is why -9 is a singularity and you must avoid it. Hence, your domain is 
(-∞,-9)U(-9,∞)

suwhitney · Answer

So, when I write (-∞,-9)U(-9,∞) I am basically saying that it can be anything EXCEPT -9?

anonymous · Answer

Yeah, exactly. That's what the -9) means. If you had the square bracket -9] you would say it can be anything up to -9, but also include -9.

suwhitney · Answer

Ok, thank you so much :)

anonymous · Answer

You're welcome. Anytime!