document.write( "Question 1138851: For each pair of functions, find fog and gof, if they exist
\n" ); document.write( "f={(-1,2),(5,6)(0,9)}
\n" ); document.write( "g={(6,0),(2,-1),(9,5)}
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Algebra.Com's Answer #756637 by MathLover1(20850)\"\" \"About 
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solve a system of three equations derived from the original three coordinate pairs\r
\n" ); document.write( "\n" ); document.write( "f={(-1,2),(5,6)(0,9)}\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29=ax%5E2%2Bbx%2Bc\"\r
\n" ); document.write( "\n" ); document.write( "(\"-1\",\"2\")
\n" ); document.write( "\"2=a%28-1%29%5E2%2B%28-1%29b%2Bc\"
\n" ); document.write( "\"2=a-b%2Bc\"..........eq.1\r
\n" ); document.write( "\n" ); document.write( "(\"5\",\"6\")
\n" ); document.write( "\"6=a%285%29%5E2%2B%285%29b%2Bc\"
\n" ); document.write( "\"6=25a%2B5b%2Bc\"..........eq.2\r
\n" ); document.write( "\n" ); document.write( "(\"0\",\"9\")
\n" ); document.write( "\"9=a%280%29%5E2%2B%280%29b%2Bc\"
\n" ); document.write( "\"c=9\"\r
\n" ); document.write( "\n" ); document.write( "go to \"2=a-b%2Bc\"..........eq.1, substitute \"c\"\r
\n" ); document.write( "\n" ); document.write( "\"2=a-b%2B9\"..........solve for \"b\"\r
\n" ); document.write( "\n" ); document.write( "..........eq.2 , substitute \"b\" and \"c\"\r
\n" ); document.write( "\n" ); document.write( "\"6=25a%2B5%28a%2B7%29%2B9\".......solve for \"a\"\r
\n" ); document.write( "\n" ); document.write( "\"6=25a%2B5a%2B35%2B9\"
\n" ); document.write( "\"6=30a%2B44\"
\n" ); document.write( "\"6-44=30a\"
\n" ); document.write( "\"a=-38%2F30\"\r
\n" ); document.write( "\n" ); document.write( "\"a=-19%2F15\"\r
\n" ); document.write( "\n" ); document.write( "go to \"b=a%2B7\"......eq.1a, substitute \"a\"\r
\n" ); document.write( "\n" ); document.write( " \"b=-19%2F15%2B7\"
\n" ); document.write( "\"b=-19%2F15%2B105%2F15\"
\n" ); document.write( "\"b=86%2F15\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "=>\"f%28x%29=-%2819%2F15%29x%5E2%2B%2886%2F15%29x%2B9\"\r
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\n" ); document.write( "\n" ); document.write( "g={(6,0),(2,-1),(9,5)} \r
\n" ); document.write( "\n" ); document.write( "\"g%28x%29=ax%5E2%2Bbx%2Bc\"\r
\n" ); document.write( "\n" ); document.write( "(\"6\",\"0\")
\n" ); document.write( "\"0=a%286%29%5E2%2B%286%29b%2Bc\"
\n" ); document.write( "\"0=36a%2B6b%2Bc\"..........eq.1\r
\n" ); document.write( "\n" ); document.write( "(\"2\",\"-1\")
\n" ); document.write( "\"-1=a%282%29%5E2%2B%282%29b%2Bc\"
\n" ); document.write( "\"-1=4a%2B2b%2Bc\"..........eq.2\r
\n" ); document.write( "\n" ); document.write( "(\"9\",\"5\")
\n" ); document.write( "\"5=a%289%29%5E2%2B%289%29b%2Bc\"
\n" ); document.write( "\"5=81a%2B9b%2Bc\"..........eq.3\r
\n" ); document.write( "\n" ); document.write( "go to
\n" ); document.write( "\"0=36a%2B6b%2Bc\"..........eq.1
\n" ); document.write( "\"-1=4a%2B2b%2Bc\"..........eq.2
\n" ); document.write( "------------------------------------------subtract\r
\n" ); document.write( "\n" ); document.write( "\"0-%28-1%29=36a-4a%2B6b-2b%2Bc-c\"
\n" ); document.write( "\"1=32a%2B4b\".........solve for \"b\"\r
\n" ); document.write( "\n" ); document.write( "\"%281-32a%29%2F4=b\"\r
\n" ); document.write( "\n" ); document.write( "\"b=1%2F4-8a\"............eq.1a\r
\n" ); document.write( "\n" ); document.write( "go to
\n" ); document.write( "\"5=81a%2B9b%2Bc\"..........eq.3
\n" ); document.write( "\"0=36a%2B6b%2Bc\"..........eq.1
\n" ); document.write( "------------------------------------------subtract
\n" ); document.write( "\"5-0=81a-36a%2B9b-6b%2Bc-c\"
\n" ); document.write( "\"5=45a%2B3b\".......solve for \"b\"
\n" ); document.write( "\"b=+5%2F3+-+15+a\"..............eq.2a\r
\n" ); document.write( "\n" ); document.write( "from eq.1a and eq.2awe have\r
\n" ); document.write( "\n" ); document.write( "\"1%2F4-8a=+5%2F3+-+15+a\"........solve for \"a\"\r
\n" ); document.write( "\n" ); document.write( "\"15a-8a=5%2F3-1%2F4\"
\n" ); document.write( "\"7a=+17%2F12\"\r
\n" ); document.write( "\n" ); document.write( "\"a=++17%2F84\"\r
\n" ); document.write( "\n" ); document.write( "go to \"b=5%2F3+-+15+a\"............eq.1a, substitute \"a\"
\n" ); document.write( "\"b=5%2F3+-+15+%2817%2F84%29\"
\n" ); document.write( "\"b=-115%2F84+\"\r
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\n" ); document.write( "\n" ); document.write( "go to \"-1=4a%2B2b%2Bc\"..........eq.2, substitute \"a\" and \"b\"\r
\n" ); document.write( "\n" ); document.write( "\"-1=4%2817%2F84%29%2B2%28-115%2F84%29%2Bc\"
\n" ); document.write( "
\n" ); document.write( "\"-1=17%2F21-115%2F42%2Bc\"\r
\n" ); document.write( "\n" ); document.write( "\"c=+-1-17%2F21%2B115%2F42\"\r
\n" ); document.write( "\n" ); document.write( "\"c=+13%2F14\"\r
\n" ); document.write( "\n" ); document.write( "\"g%28x%29=+%2817%2F84%29x%5E2-%28115%2F84%29x%2B13%2F14\"\r
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\n" ); document.write( "\n" ); document.write( "so, your functions are:
\n" ); document.write( "\"f%28x%29=-%2819%2F15%29x%5E2%2B%2886%2F15%29x%2B9\"
\n" ); document.write( "\"g%28x%29=+%2817%2F84%29x%5E2-%28115%2F84%29x%2B13%2F14\"\r
\n" ); document.write( "\n" ); document.write( "find \"f\"o\"g\"=\"f%28g%28x%29%29\" \r
\n" ); document.write( "\n" ); document.write( "\"f%28g%28x%29%29=f%28%2817%2F84%29x%5E2-%28115%2F84%29x%2B13%2F14%29\" \r
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\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "and \"g\"o\"f\"=\"g%28f%28x%29%29\" \r
\n" ); document.write( "\n" ); document.write( "\"g%28f%28x%29%29=g%28%28-19%2F15%29x%5E2%2B%2886%2F15%29x%2B9%29\" \r
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