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Given the definitions of f(x) and g(x) below, find the value of g(f(2)). {:[f(x)=x^(2)-7x+13],[g(x)=-2x+8]:} Answer:

Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of g(f(2)) g(f(2)) .\newlinef(x)=x2−7x+13g(x)=−2x+8 \begin{array}{l} f(x)=x^{2}-7 x+13 \\ 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 g(f(2)) g(f(2)) .\newlinef(x)=x2−7x+13g(x)=−2x+8 \begin{array}{l} f(x)=x^{2}-7 x+13 \\ g(x)=-2 x+8 \end{array} \newlineAnswer:
  1. Calculate f(2)f(2): First, we need to calculate the value of f(2)f(2) by substituting xx with 22 in the function f(x)f(x).\newlinef(2)=(2)2−7(2)+13f(2) = (2)^2 - 7(2) + 13
  2. Perform f(2)f(2) calculation: Now, perform the calculation for f(2)f(2).f(2)=4−14+13f(2) = 4 - 14 + 13
  3. Simplify f(2)f(2) expression: Simplify the expression to find the value of f(2)f(2).f(2)=4−14+13=3f(2) = 4 - 14 + 13 = 3
  4. Find g(f(2))g(f(2)): Next, we need to find the value of g(f(2))g(f(2)). Since we have found that f(2)=3f(2) = 3, we substitute this value into g(x)g(x).\newlineg(f(2))=g(3)=−2(3)+8g(f(2)) = g(3) = -2(3) + 8
  5. Calculate g(3)g(3): Finally, perform the calculation for g(3)g(3).\newlineg(3)=−2(3)+8=−6+8g(3) = -2(3) + 8 = -6 + 8
  6. Simplify g(3)g(3) expression: Simplify the expression to find the value of g(3)g(3).g(3)=−6+8=2g(3) = -6 + 8 = 2

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