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Given the definitions of f(x) and g(x) below, find the value of g(f(-4)). {:[f(x)=2x+13],[g(x)=x^(2)-3x+8]:} Answer:

Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of g(f(−4)) g(f(-4)) .\newlinef(x)=2x+13g(x)=x2−3x+8 \begin{array}{l} f(x)=2 x+13 \\ g(x)=x^{2}-3 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 g(f(−4)) g(f(-4)) .\newlinef(x)=2x+13g(x)=x2−3x+8 \begin{array}{l} f(x)=2 x+13 \\ g(x)=x^{2}-3 x+8 \end{array} \newlineAnswer:
  1. Find f(−4)f(-4): First, we need to find the value of f(−4)f(-4) by substituting −4-4 into the function f(x)f(x).\newlineCalculation: f(−4)=2(−4)+13f(-4) = 2(-4) + 13
  2. Calculate f(−4)f(-4): Now, let's perform the calculation for f(−4)f(-4).\newlineCalculation: f(−4)=2(−4)+13=−8+13=5f(-4) = 2(-4) + 13 = -8 + 13 = 5
  3. Find g(f(−4))g(f(-4)): Next, we need to find the value of g(f(−4))g(f(-4)) by substituting f(−4)f(-4) into the function g(x)g(x).\newlineSince we found that f(−4)=5f(-4) = 5, we will substitute 55 into g(x)g(x).\newlineCalculation: g(5)=(5)2−3(5)+8g(5) = (5)^2 - 3(5) + 8
  4. Calculate g(5)g(5): Now, let's perform the calculation for g(5)g(5).\newlineCalculation: g(5)=(5)2−3(5)+8=25−15+8=18g(5) = (5)^2 - 3(5) + 8 = 25 - 15 + 8 = 18

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