document.write( "Question 252676: let f(x)=3x-6 and g(x)=x-2. find the g/f and state its domain. \n" ); document.write( "

Algebra.Com's Answer #184747 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
Note: The other tutor mistakenly did f/g, not g/f.
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\n" ); document.write( " $\"%22%28g%2Ff%29%28x%29%22+=+%28x-2%29%2F%283x-6%29\"$ , $\"x%3C%3E2\"$
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document.write( "This function g/f is not defined when the denominator \r\n" );
document.write( "equals 0. The denominator would equal 0 when  \r\n" );
document.write( "which simplifies to when .  Therefore\r\n" );
document.write( "x cannot equal 2, and 2 cannot be part of the domain\r\n" );
document.write( "of g/f. However when , the right side \r\n" );
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document.write( " can be simplified to\r\n" );
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document.write( "However that cancellation cannot be made when !,\r\n" );
document.write( "since the function is undefined there, but it can be done\r\n" );
document.write( "for every other value of x.\r\n" );
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document.write( "So therefore we can express g/f in its simplest form \r\n" );
document.write( "this way:\r\n" );
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document.write( "Its graph is the green graph below.  It is the horizontal\r\n" );
document.write( "green line with a hole in it where the point (2,)\r\n" );
document.write( "is missing and that point is NOT part of the graph of g/f:\r\n" );
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document.write( "So the domain of g/f is the x-axis without a value at 2.\r\n" );
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document.write( "In set-builder notation the domain of g/f would be\r\n" );
document.write( "written .  \r\n" );
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document.write( "The graph of its domain on a number line would look just \r\n" );
document.write( "like the x-axis above only, shaded everywhere except at 2,\r\n" );
document.write( "and with an open circle at 2, like this:\r\n" );
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document.write( "-4  -3  -2  -1   0   1   2   3   4  \r\n" );
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document.write( "In interval notation this domain is written\r\n" );
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document.write( "Edwin

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