need help with domain of equations inside radicals

[wingedone]

I do not understand domain, and I have to find the domain of this:

y= square root of(9-x^2) + square root of(1-x^2)

my answer key says that the domain is [1,3] but I do not know why. Can anyone explain this to me?

 

[tkhunny]

You are not yet in Complex Numbers. This means that stuff under a square root MUST be Positive or Zero.

So, 1 - x^2 >= 0 or 1 >= x^2 so |x| <= 1

Similarly, 9 - x^2 >= 0 or 9 >= x^2 so |x| <= 3

Clearly, then, the answer key is simply wrong. It should be [-1,1]. Try x = 2 and prove the answer key wrong!

 

[wingedone]

you're right, it doesn't work! no wonder it didn't make any sense. ahh, I hate it when the answers are wrong. Thank you for your help!!! =]