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# ​ HELP ASAP!!!

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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