document.write( "Question 551688: if f(g(x)) = 6x^3, what are possibilities for f,g?\r
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Algebra.Com's Answer #359850 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Sometimes multiple choice questions are best solved by trying out each\r\n" );
document.write( "choice to find out which one works:\r\n" );
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document.write( "Notice what is different about the notation f(x) and the notation f(g(x))\r\n" );
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document.write( "If you replace the x in f(x), by g(x), you get f(g(x))\r\n" );
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document.write( "So what we do with the right sides of f(x) and g(x) is the same. We replace\r\n" );
document.write( "x in the right side of the f(x) equation by the ENTIRE RIGHT SIDE of the\r\n" );
document.write( "g(x) equation.\r\n" );
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document.write( "if f(g(x)) = 6x³, what are possibilities for f,g?\r\n" );
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document.write( "Let's see if (a) is the correct answer:\r\n" );
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document.write( "a) f(x) = 6x, g(x) = x²\r\n" );
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document.write( "Let's substitute the right side of the g(x) equation for x\r\n" );
document.write( "in the f(x) equation:\r\n" );
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document.write( "f(g(x)) = 6(x²) = 6x² \r\n" );
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document.write( "So (a) is not correct.\r\n" );
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document.write( "Let's see if (b) is the correct answer:\r\n" );
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document.write( "b) f(x) = x², g(x) = 6x\r\n" );
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document.write( "Let's substitute the right side of the g(x) equation for x\r\n" );
document.write( "in the f(x) equation:\r\n" );
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document.write( "f(g(x)) = (6x)² = 36x²\r\n" );
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document.write( "So (b) is not correct.\r\n" );
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document.write( "Let's see if (c) is the correct answer:\r\n" );
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document.write( "c) f(x) = 2x, g(x) = 3x³\r\n" );
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document.write( "Let's substitute the right side of the g(x) equation for x\r\n" );
document.write( "in the f(x) equation:\r\n" );
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document.write( "f(g(x)) = 2(3x³) = 6x³\r\n" );
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document.write( "So (c) is the correct choice.  \r\n" );
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document.write( "We have the answer but let's follow through and see why (d) isn't correct:\r\n" );
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document.write( "Let's see if (d) is the correct answer:\r\n" );
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document.write( "d) f(x) = 3x^3, g(x) = 2x\r\n" );
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document.write( "Let's substitute the right side of the g(x) equation for x\r\n" );
document.write( "in the f(x) equation:\r\n" );
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document.write( "f(g(x)) = 3(2x)³ = 3·2³x³ = 3·8x³ = 24x³\r\n" );
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document.write( "So (d) is not correct.\r\n" );
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document.write( "Answer (c)\r\n" );
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document.write( "Edwin
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