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Set the argument of the function equal to 3 and solve for x.

Computer Science

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Step-by-step solution

3 steps

To find f(3)f(3) given the function f(x+1)=3x2−x+4f(x+1) = 3x^2 - x + 4, we first need to determine the value of xx that makes the argument of the function equal to 3.

  1. Set the argument of the function equal to 3 and solve for xx.

    x+1=3x+1 = 3 x=3−1x = 3 - 1 x=2x = 2

  2. Substitute x=2x=2 into the expression for f(x+1)f(x+1).

    f(3)=3(2)2−(2)+4f(3) = 3(2)^2 - (2) + 4

  3. Perform the calculations.

    f(3)=3(4)−2+4f(3) = 3(4) - 2 + 4 f(3)=12−2+4f(3) = 12 - 2 + 4 f(3)=10+4f(3) = 10 + 4 f(3)=14f(3) = 14

    Comparing this result with the given options:
    A) 10
    B) 16
    C) 12
    D) 14

    The calculated value matches option D.

    The final answer is D) 14\boxed{\text{D) 14}}.

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