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\(Let $f(x) = 3x^2-2,$ and let $g(x)$ be a function such that $g(f(x)) = x^2 + x +1$. Find the sum of all possible values of $g(25)$. \)

 
 Aug 5, 2022
 #1
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The sum of all possible values of g(25) is 15.

 
 Aug 5, 2022
 #2
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How did you get that? It is incorrect.

 
Guest Aug 5, 2022
 #3
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We have \(25 = f(x) \).

 

Substituting what we know for \(f(x)\), we have the following equation: \(3x^2 - 2 = 25\)

 

Solving, we find \(x = \pm 3\).

 

If \(x = 3\), the value of \(g(f(x)) = 3^3 + 3 + 1 = 13\) and if \(x = -3\)\(g(f(x)) = (-3)^2 - 3 + 1 = 7\)

 

So, the sum of all possible values is \(13 + 7 = \color{brown}\boxed{20}\)

 
 Aug 6, 2022

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