SOLUTION: find the domain of: Squere root of (9 - X^2)

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Question 548533: find the domain of:
Squere root of (9 - X^2)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%289-x%5E2%29 exists only when 9-x%5E2%3E=0
Factoring, we find that
9-x%5E2=%283-x%29%283%2Bx%29
The zeros of that(polynomial) expression are x=3 and x=-3
At each of those points, one (and only one) of the factors changes sign, and the expression changes sign.
For x=0, 9-x%5E2=9-0%5E2=9-0=9%3E0
So 9-x%5E2%3E=0 for -3%3C=x%3C=3, and the domain of the function is only those values of x, in other words, the closed interval [-3,3].