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Given the definitions of f(x) and g(x) below, find the value of g(f(0)). {:[f(x)=3x^(2)+x+11],[g(x)=-3x-7]:} Answer:

Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of g(f(0)) g(f(0)) .\newlinef(x)=3x2+x+11g(x)=−3x−7 \begin{array}{l} f(x)=3 x^{2}+x+11 \\ g(x)=-3 x-7 \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 g(f(0)) g(f(0)) .\newlinef(x)=3x2+x+11g(x)=−3x−7 \begin{array}{l} f(x)=3 x^{2}+x+11 \\ g(x)=-3 x-7 \end{array} \newlineAnswer:
  1. Find f(0)f(0): First, we need to find the value of f(0)f(0) by substituting x=0x = 0 into the function f(x)f(x).
    f(0)=3(0)2+(0)+11f(0) = 3(0)^2 + (0) + 11
    f(0)=0+0+11f(0) = 0 + 0 + 11
    f(0)=11f(0) = 11
  2. Calculate g(f(0))g(f(0)): Now that we have f(0)=11f(0) = 11, we need to find the value of g(f(0))g(f(0)) by substituting f(0)f(0) into the function g(x)g(x).
    g(f(0))=g(11)g(f(0)) = g(11)
    g(11)=−3(11)−7g(11) = -3(11) - 7
    g(11)=−33−7g(11) = -33 - 7
    g(11)=−40g(11) = -40

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