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Given the definitions of f(x) and g(x) below, find the value of f(g(-2)). {:[f(x)=3x^(2)+x+7],[g(x)=2x+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)=3x2+x+7g(x)=2x+8 \begin{array}{l} f(x)=3 x^{2}+x+7 \\ g(x)=2 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)=3x2+x+7g(x)=2x+8 \begin{array}{l} f(x)=3 x^{2}+x+7 \\ g(x)=2 x+8 \end{array} \newlineAnswer:
  1. Find g(−2)g(-2): First, we need to find the value of g(−2)g(-2) by substituting xx with −2-2 in the function g(x)g(x).\newlineCalculation: g(−2)=2(−2)+8=−4+8=4g(-2) = 2(-2) + 8 = -4 + 8 = 4
  2. Substitute into f(x)f(x): Now that we have g(−2)=4g(-2) = 4, we substitute this value into the function f(x)f(x) to find f(g(−2))f(g(-2)).
    Calculation: f(g(−2))=f(4)=3(4)2+4+7=3(16)+4+7=48+4+7=59f(g(-2)) = f(4) = 3(4)^2 + 4 + 7 = 3(16) + 4 + 7 = 48 + 4 + 7 = 59

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