Matematika

Pertanyaan

Jika f(x) = -2x+4/x-6; x ¥ 6, maka f^-1(x) =

2 Jawaban

  • jika gini → f(x) = (-2x + 4)/(x - 6)
    bisa pake rumus,ato bertahap
    y = (-2x + 4)/(x - 6)
    y(x + 6) = -2x + 4
    xy + 6y = -2x + 4
    xy + 2x = 4 - 6y
    x(y + 2) = 4 - 6y
    x = (4 - 6y)/(y + 2)
    invers gnti y dengan x
    f^-1(x) = (4 - 6x)/(x + 2)
  • (-2x + 4)/(x - 6) = y
    xy - 6y = -2x + 4
    xy + 2x = 6y + 4
    x(y + 2) = 6y + 4
    x = (6y + 4)/(y + 2)
    f^-1(x) = (6x + 4)/(x + 2) ; x ≠ -2

    Atau jika f(x) = (ax + b)/(cx + d) => f^-1(x) = (-dx + b)/(cx - a)
    f(x) = (-2x + 4)/(x - 6) => f^-1(x) = (6x + 4)/(x + 2) ; x ≠ -2

    x + 2 ≠ 0 => x ≠ -2

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