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Let $f(x)=x^2-7x+18$ and let $g(f(x))=2x+3$. What is the sum of all possible values of $g(8)$?

 Jul 19, 2020
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Let f(x)=x^2-7x+18 and let g(f(x))=2x+3. What is the sum of all possible values of g(8)?

 

We have f(x) = 8, so x2 - 7x + 18 = 8  or  x2​ - 7x + 10 = 0 which factorises as: (x - 2)(x - 5) = 0

Hence x = 2 and x = 5 are two solutions for x

 

So g(2) = 7  and g(5) = 13  the sum of which is 20.

 Jul 19, 2020

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