Matematika

Pertanyaan

jika f(x) = x2 - 2x + 4 dan g(x) = x+3 maka nilai x yang memenuhi (g 0 f)(x) = 6 adalah

2 Jawaban

  • ( g o f)(x) = g(f(x))

    g(f(x)) = (x^2 -2x + 4) + 3
    6 = x^2 - 2x + 7
    x^2 -2x + 7 - 6 = 0
    x^2 - 2x + 1 = 0
    (x - 1)(x - 1) = 0

    x - 1 = 0
    x = 1

    Nilai x = 1
  • (g○f)(x) = g○(f(x)) = 6
    = g○(x^2 - 2x + 4) = 6
    = x^2 - 2x + 4 + 3 = 6
    = x^2 - 2x + 7 = 6
    = x^2 - 2x + 7 - 6 = 0
    = x^2 - 2x + 1 = 0
    = (x - 1)(x - 1) = 0
    x - 1 = 0
    x = 1
    maka nilai x yg memenuhi (g○f)(x) = 6 adalah 1

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