Matematika

Pertanyaan

kak pliss kak saya mohon minta bantu di kumpul besok ya ampun
kak pliss kak saya mohon minta bantu di kumpul besok ya ampun

1 Jawaban

  • a)
    (gof)(x) = (g (f(x))
    = [(3x-1) + 5] / [(3x-1) - 3]
    = [3x+4]/[3x-4]

    (gof)invers (x) =  [3x+4]/[3x-4]
    y =  [3x+4]/[3x-4]
    y [ 3x-4] = 3x+4
    3xy - 4y = 3x + 4
    3xy - 3x = 4 + 4y
    x [3y - 3] = 4+4y
    x = [4+4y]/[3y-3]

    (gof) inv (x) = [4+4x]/[3x-3]

    b)
    f (x) = 3x -1
    y = 3x - 1
    y+1 = 3x
    x= [y+1] / 3

    f inv (x) = [x+1] / 3

    g(x) = x+5 / x-3
    y = x + 5 / x-3
    y(x-3) = x+5
    xy - 3y = x+5
    xy - x = 5 + 3y
    x ( y - 1) = 5 + 3y
    x = [5+3y]/[y-1]
    g inv (x) = [5+3x]/[x-1]

    (f inv 0 g inv)(5) = [(5+3x)/(x-1) +1] / 3
                              ={[(5+3x)+(x-1)]/(x-1)} / 3
                              = (4+4x) / (x-1)] / 3
                              = (4+4x) / 3(x-1)
                              = (4+4x) / (3x-3)
                              = (4 + 4.5) / (3.5 -3)
                              = 24 / 12
                              = 2