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Given the definitions of f(x) and g(x) below, find the value of g(f(2)). {:[f(x)=-5x+3],[g(x)=2x^(2)+5x-14]:} 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)=−5x+3g(x)=2x2+5x−14 \begin{array}{l} f(x)=-5 x+3 \\ g(x)=2 x^{2}+5 x-14 \end{array} \newlineAnswer:

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Solve absolute value inequalitiesright chevron icon

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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)=−5x+3g(x)=2x2+5x−14 \begin{array}{l} f(x)=-5 x+3 \\ g(x)=2 x^{2}+5 x-14 \end{array} \newlineAnswer:
  1. Find f(2)f(2): First, we need to find the value of f(2)f(2) by substituting xx with 22 in the function f(x)f(x).\newlinef(2)=−5(2)+3f(2) = -5(2) + 3
  2. Calculate f(2)f(2): Now, let's perform the calculation for f(2)f(2).\newlinef(2)=−10+3f(2) = -10 + 3\newlinef(2)=−7f(2) = -7
  3. 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)=−7f(2) = -7, we will substitute xx with −7-7 in the function g(x)g(x).\newlineg(f(2))=g(−7)=2(−7)2+5(−7)−14g(f(2)) = g(-7) = 2(-7)^2 + 5(-7) - 14
  4. Calculate g(−7)g(-7): Now, let's perform the calculation for g(−7)g(-7).
    g(−7)=2(49)+5(−7)−14g(-7) = 2(49) + 5(-7) - 14
    g(−7)=98−35−14g(-7) = 98 - 35 - 14
  5. Find g(−7)g(-7): Finally, we add and subtract the numbers to find the value of g(−7)g(-7).
    g(−7)=98−35−14g(-7) = 98 - 35 - 14
    g(−7)=63−14g(-7) = 63 - 14
    g(−7)=49g(-7) = 49

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