SOLUTION: 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).

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).
Answer by ikleyn(52793) (Show Source): You can put this solution on YOUR website!
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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).
~~~~~~~~~~~~~~

Such polynomial function g(x) DOES NOT EXIST.

Proof

    Had this polynomial function g(x) be linear (of the first degree polynomial), then the composition f(g(x)) 
    would be a polynomial of the second degree, but it is not.


    Had this polynomial function g(x) be quadratic (of the second degree polynomial), then the composition f(g(x)) 
    would be a polynomial of the fourth degree, but it is not.

The proof is completed.

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