document.write( "Question 109091: Given h(x), find a pair of functions f and g such that h(x) = fgg(x):\r
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Algebra.Com's Answer #79556 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Given h(x), find a pair of functions f and g such that h(x) = fgg(x):\r\n" );
document.write( "h(x) = square root . \r\n" );
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document.write( "Pick g(x) as any expression in x from the whole expression\r\n" );
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document.write( "such that if you were to substitute u for that expression,\r\n" );
document.write( "there will be no x's left.\r\n" );
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document.write( "Suppose we pick u to be , then we replace both\r\n" );
document.write( "the 's by u and get\r\n" );
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document.write( "  \r\n" );
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document.write( "g(x) is simply equal to what we picked u to be, that is,\r\n" );
document.write( "g(x) =  \r\n" );
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document.write( "To get f(x) we substitute x for u in\r\n" );
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document.write( "and get \r\n" );
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document.write( "So  \r\n" );
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document.write( "f(x) =  \r\n" );
document.write( "g(x) =  \r\n" );
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document.write( "Checking:\r\n" );
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document.write( "h(x) = fgg(x) = f(g(x)) = f() =  .\r\n" );
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document.write( "Edwin

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