document.write( "Question 1077352: find the domain for h(x)= square root of (13+x) \n" ); document.write( "

Algebra.Com's Answer #691860 by jim_thompson5910(35256) $\"\"$ $\"About$

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The stuff under the square root (known as the radicand) cannot be negative. So that means that the \"13+x\" must be 0 or a positive value.\r
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\n" ); document.write( "\n" ); document.write( "Forcing 13+x to be 0 or positive means $\"13%2Bx%3E=0\"$ . Subtract 13 from both sides and we'll end up with $\"x+%3E=+-13\"$ \r
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\n" ); document.write( "\n" ); document.write( "Saying $\"x+%3E=+-13\"$ is the same as saying \"x can be any number as long as it's -13 or larger\". This forms what is known as the domain. The domain is the set of allowed input x values of a function. It's a rule to make sure that no errors occur. If we plug x = -14, which is NOT -13 or larger, then we run into issues of taking the square root of a negative number.\r
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\n" ); document.write( "\n" ); document.write( "So the domain is the set of all real numbers x such that $\"x+%3E=+-13\"$ \r
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\n" ); document.write( "\n" ); document.write( "Your teacher may want you to write this in interval notation. If so, then you would write [-13, infinity) where you replace \"infinity\" with the infinity symbol if needed. Notice how I placed a square bracket next to -13. This tells the reader \"include -13 in the interval\". The curved parenthesis means \"exclude the endpoint from the interval\". \r
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\n" ); document.write( "\n" ); document.write( "Note: infinity or -infinity cannot be included because it's not a number. It's impossible to get to infinity. This is why infinity and -infinity will have curved parenthesis. This is a rule you should memorize. \n" ); document.write( "

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