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# Algebra

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Let f(x)=x^2-6x+4 and let g(f(x))=2x+3. What is the sum of all possible values of g(8)?

May 20, 2022

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To get g(8), we must force f(x) = 8 to happen.

When f(x) = 8,

$$x^2 - 6x - 4 = 0\\ x = 3 \pm \sqrt{13}$$

Then g(8) is either 2(3 + sqrt(13)) + 3 or 2(3 - sqrt(13)) + 3. Now it is your turn to simplify these expressions.

May 20, 2022