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Evaluate the inner function g(x) at x = -1.

Computer Science

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Answer

B

Step-by-step solution

2 steps
  1. Evaluate the inner function g(x)g(x) at x=−1x = -1.

    The function g(x)g(x) is given by g(x)=3x−1g(x) = 3x - 1.
    Substitute x=−1x = -1 into g(x)g(x):

    g(−1)=3(−1)−1g(-1) = 3(-1) - 1 g(−1)=−3−1g(-1) = -3 - 1 g(−1)=−4g(-1) = -4
  2. Evaluate the outer function f(x)f(x) at the result from Step 1, which is f(−4)f(-4).

    The function f(x)f(x) is given by f(x)=x2+2f(x) = x^2 + 2.
    Substitute x=−4x = -4 into f(x)f(x):

    f(−4)=(−4)2+2f(-4) = (-4)^2 + 2 f(−4)=16+2f(-4) = 16 + 2 f(−4)=18f(-4) = 18

    The value of fg(−1)fg(-1) is 18.

    The correct option is B.

    B\boxed{\text{B}}
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