document.write( "Question 783530: Find the specified domain\r
\n" ); document.write( "\n" ); document.write( "For f(x)=2x-5 and g(x)=√(x+6), what is the domain of f o g?\r
\n" ); document.write( "\n" ); document.write( "This is how I worked it out but I am not sure this is correct.\r
\n" ); document.write( "\n" ); document.write( "f(g(x))=2√(x+6)-5\r
\n" ); document.write( "\n" ); document.write( "x+6=0
\n" ); document.write( "x=-6\r
\n" ); document.write( "\n" ); document.write( "Domain= (-∞, -6)∪(-6, ∞) \n" ); document.write( "

Algebra.Com's Answer #476815 by jim_thompson5910(35256) $\"\"$ $\"About$

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You are making the mistake of thinking \"I cannot divide by zero, so set x+6 equal to zero to find the values of x that aren't allowed\". This would work if the equation was y = 1/(x+6), but it's nothing like this\r
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\n" ); document.write( "\n" ); document.write( "What you need to do is solve $\"x%2B6%3E=0\"$ (see note below) for x to get $\"x+%3E=+-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the domain is really [-6, ∞)\r
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\n" ); document.write( "\n" ); document.write( "Note: remember you cannot take the square root of a negative number, so that's why the radicand $\"x%2B6\"$ must be positive or 0, so that's why you must solve $\"x%2B6%3E=0\"$ for x \n" ); document.write( "

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