document.write( "Question 477204: What are the domain and range of $\"+y+=sqrt%28%28x%2B4%29%2F%28x%5E2-5%29%29\"$ \r
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Algebra.Com's Answer #327114 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "You have to avoid a zero denominator so we start with the restriction:

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\n" ); document.write( "\n" ); document.write( "Next, note that on the interval

, but since

0\"> on this same interval,

on that interval. Since

is undefined for

, the interval

must be excluded from the domain.\r
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\n" ); document.write( "\n" ); document.write( "On the interval

\ 0\"> and

, hence

on that interval, and the function is again undefined. Hence, exclude

from the domain.\r
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\n" ); document.write( "\n" ); document.write( "So the domain is all real numbers except real numbers in the two excluded ranges:\r
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\n" ); document.write( "\n" ); document.write( "Domain:

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\n" ); document.write( "\n" ); document.write( "Since this is a positive square root and we have shown that there is a value in the domain, namely -4 that results in a zero value for the function, the range is

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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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