document.write( "Question 151896: I need to state the domain of the following.
\n" ); document.write( "A) $\"g%28x%29=5x%2F%28x%5E2%2B25%29\"$ \r
\n" ); document.write( "\n" ); document.write( "B) $\"f%28x%29=sqrt%28x%2B6%29\"$ \r
\n" ); document.write( "\n" ); document.write( "C) $\"k%28t%29=5t%5E2-6t%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "D) $\"k%28x%29=%283x%2B3%29%2F%28x%2B2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "E) $\"m%28x%29=5x-7\"$ \r
\n" ); document.write( "\n" ); document.write( "Please help. I am having trouble understanding this. \n" ); document.write( "

Algebra.Com's Answer #111690 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
I need to state the domain of the following.
\n" ); document.write( "A) $\"g%28x%29=5x%2F%28x%5E2%2B25%29\"$ \r
\n" ); document.write( "\n" ); document.write( "B) $\"f%28x%29=sqrt%28x%2B6%29\"$ \r
\n" ); document.write( "\n" ); document.write( "C) $\"k%28t%29=5t%5E2-6t%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "D) $\"k%28x%29=%283x%2B3%29%2F%28x%2B2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "E) $\"m%28x%29=5x-7\"$
\n" ); document.write( "

\r\n" );
document.write( "The domain is the set of all real numbers which can be\r\n" );
document.write( "substituted for x and there will be a real value of the \r\n" );
document.write( "function. \r\n" );
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document.write( "1. If there are no roots with an even index, or denominators \r\n" );
document.write( "containing the variables then the domain is always (, ). \r\n" );
document.write( "This domain graphed on a number line is:\r\n" );
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document.write( "<========================================================>\r\n" );
document.write( " -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 \r\n" );
document.write( "\r\n" );
document.write( "In other words, the whole number line is shaded.  It is the\r\n" );
document.write( "same as saying \"any real number may be substituted for x and\r\n" );
document.write( "a defined real number will be obtained.\r\n" );
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document.write( "2. If there is a denominator containing a variable, set the \r\n" );
document.write( "denominator equal to zero and solve this equation for the \r\n" );
document.write( "variable.  The real value (or these real values), if any are \r\n" );
document.write( "places where there is a vertical asymptote.  These must be \r\n" );
document.write( "deleted from the (, ) domain.\r\n" );
document.write( "\r\n" );
document.write( "3. If there is an even root containing a variable, set the \r\n" );
document.write( "expression under the radical less than 0.  Solve this \r\n" );
document.write( "inequality. The solution set must be deleted from the \r\n" );
document.write( "(, ) domain.\r\n" );
document.write( "\r\n" );
document.write( "Your problems:\r\n" );
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document.write( "A) \r\n" );
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document.write( "This is case 2.  So we set the denominator = 0\r\n" );
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document.write( "  \r\n" );
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document.write( "This has no real solution, since the left side is always \r\n" );
document.write( "positive and can never equal 0.  So there are no vertical \r\n" );
document.write( "asymptotes, so we have nothing to delete from the (, )\r\n" );
document.write( "domain. Therefore the domain is (, ). \r\n" );
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document.write( "B) \r\n" );
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document.write( "This is case 3, since square root is an even radical, so \r\n" );
document.write( "we solve the inequality:\r\n" );
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document.write( " which has solution \r\n" );
document.write( "\r\n" );
document.write( "Graphed on a number line this inequality is:\r\n" );
document.write( "\r\n" );
document.write( "<==========o---------------------------------------------\r\n" );
document.write( " -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 \r\n" );
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document.write( "So we delete this from the (, )\r\n" );
document.write( "domain below\r\n" );
document.write( " \r\n" );
document.write( "<========================================================>\r\n" );
document.write( " -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9\r\n" );
document.write( "\r\n" );
document.write( "and that leaves this graph:\r\n" );
document.write( "\r\n" );
document.write( "<----------@=============================================>\r\n" );
document.write( " -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9  \r\n" );
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document.write( "which means that the domain of f(x) is [-6,).\r\n" );
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document.write( "C) k(t)=5t^2-6t+2\r\n" );
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document.write( "This is case 1.  There are no roots with even index or \r\n" );
document.write( "denominators containing a variable.  Therefore the solution \r\n" );
document.write( "is simply\r\n" );
document.write( "\r\n" );
document.write( "<========================================================>\r\n" );
document.write( " -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9\r\n" );
document.write( "\r\n" );
document.write( "or (, )\r\n" );
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document.write( "  \r\n" );
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document.write( "D) \r\n" );
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document.write( "This is case 2.  So we set the denominator = 0\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "\r\n" );
document.write( "This has one real solution, .  So there is a \r\n" );
document.write( "vertical asymptote at  so we must delete from the \r\n" );
document.write( "(, ) domain. So we delete \r\n" );
document.write( "this one point from the (, )\r\n" );
document.write( "domain below:\r\n" );
document.write( " \r\n" );
document.write( "<========================================================>\r\n" );
document.write( " -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9\r\n" );
document.write( "\r\n" );
document.write( "and that leaves this graph:\r\n" );
document.write( "      \r\n" );
document.write( "<======================o=================================>\r\n" );
document.write( " -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9\r\n" );
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document.write( "and this in interval notation is\r\n" );
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document.write( "(, ) U (, )\r\n" );
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document.write( "E) \r\n" );
document.write( "This is case 1.  There are no roots with even index or \r\n" );
document.write( "denominator containing a variable.  Therefore the solution \r\n" );
document.write( "is simply\r\n" );
document.write( "\r\n" );
document.write( "<========================================================>\r\n" );
document.write( " -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9\r\n" );
document.write( "\r\n" );
document.write( "or (, )\r\n" );
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document.write( "Edwin

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