Matematika

Pertanyaan

kak, minta tolong nomor 2 ya,, yang f(2016) itu.,,
kak, minta tolong nomor 2 ya,, yang f(2016) itu.,,

1 Jawaban

  • f(x) + 2x f(1/x) = 3(x + 1) ............ (1)

    Jika x nya diganti dengan 1/x maka
    f(1/x) + 2.1/x f(1/(1/x)) = 3(1/x + 1) ===> kali x
    x f(1/x) + 2f(x) = 3x(1/x + 1)
    2f(x) + x f(1/x) = 3(1 + x) ........... (2)
    Eliminasi (1) dan (2)
    f(x) + 2x f(1/x) = 3(x + 1) ===> kali 1
    2f(x) + x f(1/x) = 3(1 + x) ===> kali 2

    f(x) + 2x f(1/x) = 3(x + 1)
    4f(x) + 2x f(1/x) = 6(x + 1)
    ---------------------------------- --
    -3 f(x) = -3 (x + 1)
    f(x) = x + 1
    Jadi f(2016) = 2016 + 1 = 2017