Matematika

Pertanyaan

Tentukan rumus fungsi invers dari
a. F(x)=5^2x+1
b. F(x)=3^-2x+4-5

1 Jawaban

  • a. f(x) = 5^2x + 1
    => y = 5^2x + 1
    => y - 1 = 5^2x
    => log(y-1) = log5^2x
    => log(y-1) = 2x log5
    => 5'log(y-1) = 2x
    => x = 5'log(y-1)
    => f invers x = 5'log(x-1)

    b. f(x) = 3^-2x+4 - 5
    => y = 3^-2x+4 - 5
    => y+5 = 3^-2x+4
    => log(y+5) = log(3^-2x+4)
    => log(y+5) = -2x+4 log3
    => 3'log(y+5)= -2x+4
    => 3'log(y+5) - 4 = -2x
    => x = 4 - 3'log(y+5)
    f invers x = 4 - 3'log(x+5)

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