Matematika

Pertanyaan

Diketahui f(1)=2 dan f(x+2)=3f(x) nilai dari f(2.015) adalah

2 Jawaban

  • f(1) = 2
    f(3) = 6
    f(2.015) = 4.030
  • f(1) = 2
    f(x + 2) = 3f(x)
    x = 1 => f(1 + 2) = 3f(1) => f(3) = 3(2) => f(3) = 6 ====> f(2.1 + 1) = 2 . 3^1
    x = 3 => f(3 + 2) = 3f(3) => f(5) = 3(6) => f(5) = 18 ==> f(2.2 + 1) = 2 . 3^2
    x = 5 => f(5 + 2) = 3f(5) => f(7) = 3(18) => f(7) = 54 => f(2.3 + 1) = 2 . 3^3
    x = 7 => f(7 + 2) = 3f(7) => f(9) = 3(54) => f(9) = 162 => f(2.4 + 1) = 2 . 3^4

    f(2015) = f(2n + 1)
    2n + 1 = 2015 => 2n = 2014 => n = 1.007
    f(2015) = f(2 . 1007 + 1) = 2 . 3^1007

    ^ = pangkat

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