Matematika

Pertanyaan

Diketahui f(x) =2x-1 / x+1, g (x) =x^2-1, dan h(x) =3x+5
Tentukan:
(h^-1 o f^-1)(x)

1 Jawaban

  • FungSI KompoSISI
    ---------------------------


           f (x) = (2x - 1)/(x + 1)
               y = (2x - 1)/(x + 1)
       xy + y = 2x - 1
      xy - 2x = -1 - y
     x (y - 2) = -1 - y
               x  = (-1 -y)/(y - 2)
       f^-1 (x) = (-1 - x)/(x - 2)


    h (x)      = 3x + 5
         y      = 3x + 5
    y - 5      = 3x
    (y - 5)/3 = x
    (x - 5)/3 = h^-1 (x)


    (f^-1 o h^-1) (x) = f^-1(h^-1) (x)
                              = (-1 - ((x - 5)/3))/((x -5)/3) - 2)
                              = (-3x + 6)/(3x - 33)



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