Matematika

Pertanyaan

jika f(x) = 2x-3 dan g(x) = 1/3x+1 untuk x ≠ -1/3 maka (g•f)–¹(x-1/2)...

1 Jawaban

  • gof(x) = 1 / {3(2x - 3)+1}
    gof(x) = 1 / {6x - 8}
    y = 1 / 6x - 8
    y(6x - 8) = 1
    6xy - 8y = 1
    6xy = 8y + 1
    x = (8y + 1) / 6y
    (gof)-¹(x) = (8x + 1) / 6x
    (gof)-¹((x-1)/2) = (8(x-1 / 2) + 1) / 6(x-1 / 2)
    = (4x - 4 + 1) / (3x - 3)
    = (4x - 3) / (3x - 3)

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