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Given the definitions of f(x) and g(x) below, find the value of g(f(-1)). {:[f(x)=x^(2)-3x-10],[g(x)=3x-10]:} Answer:

Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of g(f(−1)) g(f(-1)) .\newlinef(x)=x2−3x−10g(x)=3x−10 \begin{array}{l} f(x)=x^{2}-3 x-10 \\ g(x)=3 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(−1)) g(f(-1)) .\newlinef(x)=x2−3x−10g(x)=3x−10 \begin{array}{l} f(x)=x^{2}-3 x-10 \\ g(x)=3 x-10 \end{array} \newlineAnswer:
  1. Given Functions: We are given two functions:\newlinef(x)=x2−3x−10f(x) = x^2 - 3x - 10\newlineg(x)=3x−10g(x) = 3x - 10\newlineWe need to find the value of g(f(−1))g(f(-1)). First, we will calculate f(−1)f(-1).
  2. Calculate f(−1)f(-1): Substitute x=−1x = -1 into the function f(x)f(x).
    f(−1)=(−1)2−3(−1)−10f(-1) = (-1)^2 - 3(-1) - 10
    Calculate the value of f(−1)f(-1).
    f(−1)=1+3−10f(-1) = 1 + 3 - 10
    f(−1)=4−10f(-1) = 4 - 10
    f(−1)=−6f(-1) = -6
  3. Calculate g(f(−1))g(f(-1)): Now that we have the value of f(−1)f(-1), we will substitute it into the function g(x)g(x) to find g(f(−1))g(f(-1)).\newlineSubstitute f(−1)=−6f(-1) = -6 into g(x)g(x).\newlineg(f(−1))=g(−6)g(f(-1)) = g(-6)\newlineg(−6)=3(−6)−10g(-6) = 3(-6) - 10\newlineCalculate the value of g(−6)g(-6).\newlineg(−6)=−18−10g(-6) = -18 - 10\newlinef(−1)f(-1)00

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