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Given the definitions of f(x) and g(x) below, find the value of f(g(2)). {:[f(x)=-3x-1],[g(x)=3x^(2)-6x+8]:} Answer:

Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of f(g(2)) f(g(2)) .\newlinef(x)=−3x−1g(x)=3x2−6x+8 \begin{array}{l} f(x)=-3 x-1 \\ g(x)=3 x^{2}-6 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(2)) f(g(2)) .\newlinef(x)=−3x−1g(x)=3x2−6x+8 \begin{array}{l} f(x)=-3 x-1 \\ g(x)=3 x^{2}-6 x+8 \end{array} \newlineAnswer:
  1. Find g(2)g(2): First, we need to find the value of g(2)g(2) using the definition of g(x)g(x).\newlineg(x)=3x2−6x+8g(x) = 3x^2 - 6x + 8\newlineSo, g(2)=3(2)2−6(2)+8g(2) = 3(2)^2 - 6(2) + 8
  2. Calculate g(2)g(2): Now, let's calculate g(2)g(2).
    g(2)=3(4)−12+8g(2) = 3(4) - 12 + 8
    g(2)=12−12+8g(2) = 12 - 12 + 8
    g(2)=8g(2) = 8
  3. Use g(2)g(2) for f(g(2))f(g(2)): Next, we use the value of g(2)g(2) to find f(g(2))f(g(2)) using the definition of f(x)f(x).
    f(x)=−3x−1f(x) = -3x - 1
    So, f(g(2))=f(8)=−3(8)−1f(g(2)) = f(8) = -3(8) - 1
  4. Calculate f(8)f(8): Finally, we calculate f(8)f(8).\newlinef(8)=−3(8)−1f(8) = -3(8) - 1\newlinef(8)=−24−1f(8) = -24 - 1\newlinef(8)=−25f(8) = -25

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