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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(52788)   (Show Source):
You can put this solution on YOUR website! .
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).
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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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