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Given the definitions of f(x) and g(x) below, find the value of g(f(2)). {:[f(x)=2x^(2)+2x-7],[g(x)=4x+10]:} 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)=2x2+2x−7g(x)=4x+10 \begin{array}{l} f(x)=2 x^{2}+2 x-7 \\ g(x)=4 x+10 \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)=2x2+2x−7g(x)=4x+10 \begin{array}{l} f(x)=2 x^{2}+2 x-7 \\ g(x)=4 x+10 \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)=2(2)2+2(2)−7f(2) = 2(2)^2 + 2(2) - 7
  2. Calculate f(2)f(2): Now, let's perform the calculations for f(2)f(2).
    f(2)=2(4)+2(2)−7f(2) = 2(4) + 2(2) - 7
    f(2)=8+4−7f(2) = 8 + 4 - 7
    f(2)=12−7f(2) = 12 - 7
    f(2)=5f(2) = 5
  3. Find g(f(2))g(f(2)): Next, we need to find the value of g(f(2))g(f(2)) by substituting f(2)f(2) into the function g(x)g(x). Since we found that f(2)=5f(2) = 5, we will substitute xx with 55 in the function g(x)g(x). g(f(2))=g(5)=4(5)+10g(f(2)) = g(5) = 4(5) + 10
  4. Calculate g(5)g(5): Finally, let's perform the calculations for g(5)g(5).
    g(5)=4(5)+10g(5) = 4(5) + 10
    g(5)=20+10g(5) = 20 + 10
    g(5)=30g(5) = 30

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