document.write( "Question 891793: Give 6 pairs of functions f and g such that ( f o g )(x)=x^2-2x+1 \n" ); document.write( "
Algebra.Com's Answer #540058 by Edwin McCravy(20059) $\"\"$ $\"About$
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document.write( "(fog)(x)=x²-2x+1 factors as (x-1)², which is also (-x+1)²\r\n" );
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document.write( "The easiest pair of functions is this one\r\n" );
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document.write( "f(x) = x², g(x) = x-1 \r\n" );
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document.write( "So choose f(x) = (ax+b)² and g(x) = cx+d\r\n" );
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document.write( "Then fog(x) = [a(cx+d)+b]²\r\n" );
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document.write( "Then fog(x) = [acx+ad+b]²    \r\n" );
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document.write( "You want that to come out to be either (x-1)² or (-x+1)²\r\n" );
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document.write( "1. Make up any number for a\r\n" );
document.write( "2. Then c will have to be either the reciprocal of a or the\r\n" );
document.write( "negative of the reciprocal of a so we'll get x if we're \r\n" );
document.write( "making (x-1)², or -x if we're making (-x+1)²\r\n" );
document.write( "3, Then we choose b to make ad+b come out to be -1 if we're\r\n" );
document.write( "making (x-1)² or +1 if we're making (-x+1)².\r\n" );
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document.write( "Here are 6 made up that way.  We can make up as many as we like.\r\n" );
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document.write( "Edwin
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