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).
~~~~~~~~~~~~~~



Such polynomial function  g(x)   DOES  NOT  EXIST.



<U>Proof</U>


<pre>
    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.
</pre>

The proof is completed.