document.write( "Question 889943: Determine the natural domains of the function of x: 5/sqrt(x^2-4) \n" ); document.write( "

Algebra.Com's Answer #538560 by Fombitz(32388) $\"\"$ $\"About$

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Two issues with regards to the function is when the denominator goes to zero since division by zero is undefined and when the argument for the square root is less than zero since that's also undefined.
\n" ); document.write( "So,
\n" ); document.write( " $\"x%5E2-4%3E0\"$
\n" ); document.write( "Two boundary points are $\"x=-2\"$ and $\"x=2\"$ .
\n" ); document.write( "We can graph the denominator,
\n" ); document.write( " $\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2-4%29\"$
\n" ); document.write( "We see that between $\"x=-2\"$ and $\"x=2\"$ inclusively, the argument for the square root would be negative or zero.
\n" ); document.write( "So the domain is,
\n" ); document.write( "( $\"-infinity\"$ , $\"-2\"$ )U( $\"2\"$ , $\"infinity\"$ )
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