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Given the definitions of f(x) and g(x) below, find the value of f(g(-9)). {:[f(x)=2x^(2)+4x-8],[g(x)=-x-8]:} Answer:

Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of f(g(−9)) f(g(-9)) .\newlinef(x)=2x2+4x−8g(x)=−x−8 \begin{array}{l} f(x)=2 x^{2}+4 x-8 \\ g(x)=-x-8 \end{array} \newlineAnswer:

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Q. Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of f(g(−9)) f(g(-9)) .\newlinef(x)=2x2+4x−8g(x)=−x−8 \begin{array}{l} f(x)=2 x^{2}+4 x-8 \\ g(x)=-x-8 \end{array} \newlineAnswer:
  1. Find g(−9)g(-9): First, we need to find the value of g(−9)g(-9) by substituting −9-9 into the function g(x)g(x).
    g(−9)=−(−9)−8g(-9) = -(-9) - 8
    g(−9)=9−8g(-9) = 9 - 8
    g(−9)=1g(-9) = 1
  2. Substitute g(−9)g(-9) into f(x)f(x): Now that we have g(−9)=1g(-9) = 1, we substitute this value into the function f(x)f(x) to find f(g(−9))f(g(-9)).
    f(g(−9))=f(1)f(g(-9)) = f(1)
    f(1)=2(1)2+4(1)−8f(1) = 2(1)^2 + 4(1) - 8
    f(1)=2(1)+4−8f(1) = 2(1) + 4 - 8
    f(1)=2+4−8f(1) = 2 + 4 - 8
    f(1)=6−8f(1) = 6 - 8
    f(x)f(x)00

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