Question 50932
what is the domain of y=sq.root of (9-x^2)

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9-x^2 must be greater than or equal to zero.
9-x^2>=0
(3-x)(3+x)>=0

Put 3 and -3 on a number line and figure out where 
 the rest of the solution set lies.
There are three intervals on the line.  Check each interval, as follows:

Interval I is (-infinity,-3), so check with x=-10.
You get (3-(-10))(3+(-10)) which is <0 so no solutions there.
Interval II is (-3,3), so check x=0.
(3-0)(3+0) is >0 so this interval is part of the solution set.
Interval III is (3,+infinity), so check with x=10.
You get (3-10)(3+10) which is <0 so no solutions there.
SOLUTION:
All x values between -3 and +3 including 3 and -3:  or   -3<=x<=0 

Cheers,
Stan H.