Matematika

Pertanyaan

Mohon bantuannya kaak Jika f(x)=x^2-2x+4 (fog)(x)=4x^2+3 g(-2)=-3 maka nilai g(-3)=?

1 Jawaban

  • f(x) = x^2 - 2x + 4
    (f○g)(x) = 4x^2 + 3
    g(-2) = -3
    g(-3) = ....???

    (f○g)(x) = 4x^2 + 3
    f(g(x)) = 4x^2 + 3
    (g(x))^2 - 2(g(x)) + 4 = 4x^2 + 3
    (g(x))^2 - 2(g(x)) = 4x^2 + 3 - 4
    (g(x))^2 - 2(g(x)) = 4x^2 - 1
    (g(x) - 1)^2 - 1 = 4x^2 - 1
    (g(x) - 1)^2 = 4x^2 - 1 + 1
    (g(x) - 1)^2 = 4x^2
    g(x) - 1 = V(4x^2)
    g(x) - 1 = 2x
    g(x) = 2x + 1

    g(x) = 2x + 1
    g(-2) = 2(-2) + 1
    g(-2) = -4 + 1
    g(-2) = -3

    g(x) = 2x + 1
    g(-3) = 2(-3) + 1
    g(-3) = -6 + 1
    g(-3) = -5

    Jadi nilai g(-3) adalah -5

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