document.write( "Question 1165365: Given that f(x)=5x^2-3x+7 and f(g(x))=5x^2/9+17x^3/3+21, find all possible values for the sum of the coefficients in the polynomial function g(x). \n" ); document.write( "

Algebra.Com's Answer #789866 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "Given that f(x)=5x^2-3x+7 and f(g(x))=5x^2/9+17x^3/3+21, find all possible values for the sum
\n" ); document.write( "of the coefficients in the polynomial function g(x).
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\n" ); document.write( "\n" ); document.write( "Such polynomial function g(x) DOES NOT EXIST.\r
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\n" ); document.write( "\n" ); document.write( "Proof\r
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document.write( "    Had this polynomial function g(x) be linear (of the first degree polynomial), then the composition f(g(x)) \r\n" );
document.write( "    would be a polynomial of the second degree, but it is not.\r\n" );
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document.write( "    Had this polynomial function g(x) be quadratic (of the second degree polynomial), then the composition f(g(x)) \r\n" );
document.write( "    would be a polynomial of the fourth degree, but it is not.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The proof is completed.\r
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