Matematika

Pertanyaan

jawablah dengan sistematis

diket f(x) = 2x -5 dan g(x) = 3x + 1
tentukan
a. (f o g)-1 (x)
b. (g-1 of-1) (-3)

1 Jawaban

  • f(x) = 2x - 5
    x = (y + 5)/2
    f⁻¹(x) = (x + 5)/2

    g(x) = 3x + 1
    x = (y - 1)/3
    g⁻¹(x) = (x - 1)/3

    a) (f o g)⁻¹(x) = g⁻¹(x + 5)/2
    = ((x + 5)/2 - 1)/3
    = (x + 3)/6

    b) (g⁻¹ o f⁻¹)(-3) = g⁻¹(- 3 + 5)/2
    = g⁻¹(1)
    = (1 - 1)/3
    = 0

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