Matematika

Pertanyaan

F(x) = 1/2x-1 g(x) = 2x +4 .Fungsi(gof)-1 (10) adalah

1 Jawaban

  • Langsung aja y

    f{f`¹(x)} = x
    1/2f`¹(x)-1 = x
    2x.f`¹(x) - x = 1
    f`¹(x) = 1+x / 2x

    g{g`¹(x)} = x
    2g`¹(x) + 4 = x
    g`¹(x) = x-4 / 2

    (gof)`¹(x) = f`¹og`¹(x)

    = f`¹{g`¹(x)}
    = 1+g`¹(x) / 2g`¹(x)
    = (1+(x-4 / 2) : 2(x-4 / 2)
    = (2+x-4)/2 : (x-4)
    = (x-2)/2 × 1/(x-4)
    = (x-2) / (2x-8)

    (gof)`¹(10) = (10-2) / (2.10 - 8) = 8/12 = ⅔

    Semoga berguna +_+

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