Domain of functions

Question

Hi, I need to know if my answers are right . 

 

f(x)= √9-x²

f(x)=√x²-9

 

For both i got [-3,∝) 

 

 

** 9-x²  and x²-9 are both under the same root**

Answer 1

Kyle,

 

Actually, your answer is wrong for both problems.

 

To find the domain for each of these functions, you must set the radicand (the expression inside the square root) to be ≥ 0, and solve for x. This is due to the fact that you cannot find the square root of a negative real number and have the answer be a real number (which I am sure you know).

 

For f(x) = √(9 - x²), you must solve 9 - x² ≥ 0. The answer is [−3, 3].

 

For f(x) = √(x² - 9), you need to solve x² − 9 ≥ 0. The answer is (-∞, 3] ∪ [3, ∞).

 

I have purposely left the details out on how to solve these inequalities. If you cannot solve them yourself, please post a reply and I will be happy to show you how.

 

Please let me know.