document.write( "Question 548533: find the domain of:
\n" ); document.write( "Squere root of (9 - X^2) \n" ); document.write( "

Algebra.Com's Answer #357293 by KMST(5328) $\"\"$ $\"About$

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$\"sqrt%289-x%5E2%29\"$ exists only when $\"9-x%5E2%3E=0\"$
\n" ); document.write( "Factoring, we find that
\n" ); document.write( " $\"9-x%5E2=%283-x%29%283%2Bx%29\"$
\n" ); document.write( "The zeros of that(polynomial) expression are $\"x=3\"$ and $\"x=-3\"$
\n" ); document.write( "At each of those points, one (and only one) of the factors changes sign, and the expression changes sign.
\n" ); document.write( "For $\"x=0\"$ , $\"9-x%5E2=9-0%5E2=9-0=9%3E0\"$
\n" ); document.write( "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]. \n" ); document.write( "

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