Matematika

Pertanyaan

tolong dibantu segera
tolong dibantu segera

1 Jawaban

  • (g o f)(x) = 4x^2 + 6x - 4
    g(f(x)) = 4x^2 + 6x - 4
    g(2x + 4) = 4x^2 + 6x - 4
    Misal (2x + 4) = a => 2x = (a - 4) => x = (a - 4)/2
    g(a) = 4((a - 4)/2)^2 + 6(a - 4)/2 - 4
    g(a) = 4 (a^2 - 8a + 16)/4 + 3(a - 4) - 4
    g(a) = a^2 - 8a + 16 + 3a - 12 - 4
    g(a) = a^2 - 5a
    g(x) = x^2 - 5x
    x^2 - 5x = y ===> kedua ruas ditambah 25/4
    x^2 - 5x + 25/4 = y + 25/4
    (x - 5/2)^2 = (4y + 25)/4
    (x - 5/2) = ±√((4y + 25)/4)
    x = 5/2 ± √(4y + 25) / 2
    x = (5 ± √(4y + 25)) / 2
    g^-1(x) = (5 ± √(4x + 25)) / 2