Matematika

Pertanyaan

diketahui f(x)= 3x/2x-3 dan g(x)= 4x+1.jika nilai (f invers bundaran g invers)(p)=1/2,nilai p adalah

1 Jawaban

  • fog(x) = f(g(x)) = f(4x + 1)= 3(4x + 1)/(2(4x + 1) - 3)
    fog(x) = y = (12x + 3)/(8x - 1)
    y(8x - 1) = 12x + 3
    8xy - y = 12x + 3
    8xy - 12x = y + 3
    x(8y - 12) = y + 3
    x = (y + 3)/(8y - 12)
    fog^-1(x) = (x + 3)/(8x - 12)
    fog^-1(p) = 1/2
    (p + 3)/(8p - 12) = 1/2
    p + 3 = (1/2)(8p - 12)
    2p + 6 = 8p - 12
    18 = 10p
    p = 9/5

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