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{:[f(x)=(1)/(x-1)],[g(x)=5x+8]:} The functions f and g are defined. What is the value of f(g(-1)) ?

f(x)=1x−1g(x)=5x+8 \begin{array}{l} f(x)=\frac{1}{x-1} \\ g(x)=5 x+8 \end{array} \newlineThe functions f f and g g are defined. What is the value of f(g(−1)) f(g(-1)) ?

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Q. f(x)=1x−1g(x)=5x+8 \begin{array}{l} f(x)=\frac{1}{x-1} \\ g(x)=5 x+8 \end{array} \newlineThe functions f f and g g are defined. What is the value of f(g(−1)) f(g(-1)) ?
  1. Find g(−1)g(-1): First, we need to find the value of g(−1)g(-1) by substituting xx with −1-1 in the function g(x)g(x).
    g(x)=5x+8g(x) = 5x + 8
    g(−1)=5(−1)+8g(-1) = 5(-1) + 8
  2. Calculate g(−1)g(-1): Now, let's perform the calculation for g(−1)g(-1).
    g(−1)=5(−1)+8g(-1) = 5(-1) + 8
    g(−1)=−5+8g(-1) = -5 + 8
    g(−1)=3g(-1) = 3
  3. Substitute into f(x)f(x): Next, we need to substitute the value of g(−1)g(-1) into the function f(x)f(x) to find f(g(−1))f(g(-1)).\newlinef(x)=1(x−1)f(x) = \frac{1}{(x - 1)}\newlinef(g(−1))=f(3)f(g(-1)) = f(3)
  4. Calculate f(3)f(3): Now, let's perform the calculation for f(3)f(3).\newlinef(3)=1(3−1)f(3) = \frac{1}{(3 - 1)}\newlinef(3)=12f(3) = \frac{1}{2}
  5. Final Result: We have found the value of f(g(−1))f(g(-1)), which is f(3)f(3), and we have calculated it to be 12\frac{1}{2}.

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