Matematika

Pertanyaan

tentukan nilai (f o h)^-1 (x)
tentukan nilai (f o h)^-1 (x)

1 Jawaban

  • f(x) = 1 / (2x - 1)
    g(x) = - 1/(x - 3)

    (fog) (x)
    = 1 / (2 (-1/(x - 3) ) - 1)
    = 1 / ( -2 / (x - 3) ) - 1)
    = 1 / ( ( - 2 - x + 3) / (x - 3))
    = 1 / (-x + 1) / (x - 3)
    = (x - 3) / (-x + 1)
    y = (x - 3) / (-x + 1)
    y(-x + 1) = x - 3
    -xy + y = x - 3
    -xy - x = -3 - y
    x (-y - 1) = -3 - y
    x = - (3 + y) / - (1 + y)
    (fog) -¹(x) = (3 + x) / (x + 1)