Matematika

Pertanyaan

Jika f(2x+4)=x dan g(3-x)=x, maka nilai f(g(1))-g(f(2)) sama dengan

2 Jawaban

  • 1. 3 - x = 1
    x = 2
    g(3 - 2) = 2
    g(1) = 2

    2. 2x + 4 = 2
    2x = -2
    x = -1
    f(2(-1) + 4) = -1
    f(2) = -1

    f(2) - g(-1)
    2 - (-1)
    = 3
  • f(2x + 4) = x
    Misal 2x + 4 = a => 2x = a - 4 => x = (a - 4)/2
    f(a) = (a - 4)/2
    f(2) = (2 - 4)/2 = (-2)/2 = -1

    g(3 - x) = x
    Misal a = 3 - x => x = 3 - a
    g(a) = 3 - a
    g(1) = 3 - 1 = 2
    g(-1) = 3 - (-1) = 4

    f(g(1)) - g(f(2)) = f(2) - g(-1) = -1 - 4 = -5

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