Matematika

Pertanyaan

tentukan invers dari fungsi fungsi berikut.

a. t(x) = 3pangkat2x - 15
b. u(x) = 2pangkat3x-pangkat9
c. w(x)= pangkat5 log (5x+125)
d q(x) = log (2x + 7) - 10

tolong jawab beserta caranya

1 Jawaban

  • a) 3^2x - 15 = y
    3^2x = y + 15
    2x = ³log (y+15)
    x = (½).³log (y+15)
    x = ³log √(y+15)
    t-¹(x) = ³log √(x+15)

    b) 2^(3x-9) = y
    3x - 9 = ²log y
    3x = ²log y + 9
    x = (⅓).²log y + 9/3
    x = (²log ³√y) + 3
    u-¹(x) = (²log ³√y) + 3

    c) ^5log (5x+125) = y
    ^5log 5x + ^5log 125 = y
    ^5log 5x + 3 = y
    ^5log 5x = y - 3
    5x = 5^(y-3)
    x = 5^(y-3)/5
    x = 5^(y-4)
    w-¹(x) = 5^(x-4)

    d) log (2x+7) - 10 = y
    log (2x+7) = y+10
    2x + 7 = 10^(y+10)
    2x = 10^(y+10) - 7
    x = {10^(y+10) - 7} / 2
    q-¹(x) = {10^(x+10) - 7} / 2

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