Matematika

Pertanyaan

jika f(x)= 3x-4 dan g(x)=3-4x.Tentukanlah (g o f) -1 dan (x) dan (f o g) -1 (x)

1 Jawaban

  • f(x) = 3x - 4
    f⁻¹(x) = (x + 4)/3
    g(x) = 3 - 4x
    g⁻¹(x) = (3 - x)/4

    (g o f)⁻¹ (x) = f⁻¹ o g⁻¹
    = f⁻¹(3 - x)/4
    = ((3 - x)/4 + 4)/3
    = (3 - x + 16)/12
    = (19 - x)/12

    (f o g)⁻¹(x) = g⁻¹ o f⁻¹
    = g⁻¹(x + 4)/3
    = (3 - (x + 4)/3)/3
    = (9 - x - 4)/9
    = (5 - x)/9

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