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Given the definitions of f(x) and g(x) below, find the value of g(f(-8)). {:[f(x)=x+13],[g(x)=x^(2)+5x-11]:} Answer:

Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of g(f(−8)) g(f(-8)) .\newlinef(x)=x+13g(x)=x2+5x−11 \begin{array}{l} f(x)=x+13 \\ g(x)=x^{2}+5 x-11 \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(−8)) g(f(-8)) .\newlinef(x)=x+13g(x)=x2+5x−11 \begin{array}{l} f(x)=x+13 \\ g(x)=x^{2}+5 x-11 \end{array} \newlineAnswer:
  1. Find f(−8)f(-8): First, we need to find the value of f(−8)f(-8) by substituting −8-8 into the function f(x)f(x).\newlineCalculation: f(−8)=(−8)+13f(-8) = (-8) + 13
  2. Calculate f(−8)f(-8): Now, we calculate the value of f(−8)f(-8).\newlineCalculation: f(−8)=−8+13=5f(-8) = -8 + 13 = 5
  3. Find g(f(−8))g(f(-8)): Next, we need to find the value of g(f(−8))g(f(-8)) by substituting f(−8)f(-8) into the function g(x)g(x).\newlineCalculation: g(f(\(-8)) = g(55) = (55)^22 + 55(55) - 1111
  4. Calculate g(5)g(5): Now, we calculate the value of g(5)g(5).\newlineCalculation: g(5)=52+5(5)−11=25+25−11g(5) = 5^2 + 5(5) - 11 = 25 + 25 - 11
  5. Find g(5)g(5): Finally, we add and subtract the numbers to find the value of g(5)g(5).\newlineCalculation: g(5)=25+25−11=50−11=39g(5) = 25 + 25 - 11 = 50 - 11 = 39

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