Matematika

Pertanyaan

diketahui f(x) = 3x-1 dan (gof)(x) = 9x² - 6x + 4 maka (fog)(x) =......?
tolong di bantu ya beserta caranya

1 Jawaban

  • (gof)(x) = 9x²-6x+4
    g(f(x)) = 9x²-6x+4
    g(3x-1) = 9x²-6x+4
    misal 3x-1 = a
    x = (a+1) : 3
    jadi
    g(a) = 9 ((a+1) : 3)² -6 ((a+1) : 3) +4
    = 9 ( (a² +2a+1) :9) - 6 ((a+1) : 3) +4
    = ( a² +2a+1) - 2(a+1) +4
    = a² +2a+1 -2a -2 +4
    = a² + 3
    g(x) = x² + 3

    nah,
    (fog)(x) = f(g(x))
    = 3( x² +3) -1
    = 3x² + 9 -1
    = 3x² + 8

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