Matematika

Pertanyaan

1. Diketahui f(x)= x²-2x-8 dan g(x) = x²+3x+2. Tentukan f(-1) dan (gof)(-1)

2.Tentukan (fog)(x) untuk x=-2 apabila f(x)=x²-4x-5 dan g(x) = 15 / x+3

2 Jawaban

  • 1) f(x) = x² - 2x - 8
    f(-1) = (-1)² - 2(-1) - 8 = 1 + 2 - 8 = -5

    g(x) = x² + 3x + 2
    (g o f)(-1) = g(f(-1)) = g(-5) = (-5)² + 3(-5) + 2 = 25 - 15 + 2 = 12

    2) g(x) = 15/(x + 3)
    => g(-2) = 15/(-2 + 3) = 15/1 = 15

    f(x) = x² - 4x - 5
    (f o g)(x) untuk x = -2
    (f o g)(-2) = f(g(-2)) = f(15) = 15² - 4(15) - 5 = 225 - 60 - 5 = 160
  • 1)
    f (x) = x² - 2x - 8
    g (x) = x² + 3x + 2

    f (-1) = (-1)
    ² - 2.(-1) - 8
           = 1 + 2 - 8
           = -5

    gof (-1) = g (f (-1))
               = g (-5)
               = (-5)² + 3.(-5) + 2
               = 25 - 15 + 2
               = 12

    2)
    f(x)=x² - 4x - 5
    g(x) = 15 / (x + 3)

    fog (-2) = f (g(-2))
                 = f (15 / (-2 + 3))
                 = f (15)
                 = 15
    ² - 4.15 - 5
                 = 225 - 60 - 5
                 = 160

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