Matematika

Pertanyaan

Mohon bantuannya nomor 3 dan 4. Terima kasih
Mohon bantuannya nomor 3 dan 4. Terima kasih

1 Jawaban

  • 3) f(x) - 2f(1 - x) = x^2 ..... (1)
    Jika x nya diganti dengan 1 - x maka diperoleh
    f(1 - x) - 2f(1 - (1 - x)) = (1 - x)^2
    f(1 - x) - 2f(1 - 1 + x) = 1 - 2x + x^2
    f(1 - x) - 2f(x) = 1 - 2x + x^2 ---------> kali 2
    2f(1 - x) - 4f(x) = 2 - 4x + 2x^2 ....... (2)

    Eliminasi 1 dan 2
    f(x) - 2f(1 - x) = x^2
    2f(1 - x) - 4f(x) = 2 - 4x + 2x^2
    --------------------------------------------- +
    -3 f(x) = 2 - 4x + 3x^2
    f(x) = (2 - 4x + 3x^2)/(-3)

    f(x) = (-3x^2 + 4x - 2)/3

    f(x) = -x^2 + 4/3 x - 2/3

    4) f(2x + 4) = x
    Misal 2x + 4 = a => 2x = a - 4 => x = (a - 4)/2
    f(a) = (a - 4)/2
    f(2) = (2 - 4)/2 = (-2)/2 = -1

    g(3 - x) = x
    Misal a = 3 - x => x = 3 - a
    g(a) = 3 - a
    g(1) = 3 - 1 = 2
    g(-1) = 3 - (-1) = 4

    f(g(1)) - g(f(2)) = f(2) - g(-1) = -1 - 4 = -5