Matematika

Pertanyaan

f(x)= 2x + 1 dan (fog)(x+1)= -2xkuadrat - 4x - 1 nilai g invers (-2) ?

1 Jawaban

  • (f ○ g)(x + 1) = f(g(x + 1))
    -2x^2 - 4x - 1 = 2(g(x + 1)) + 1
    2(g(x + 1)) = -2x^2 - 4x - 1 - 1
    g(x + 1) = (-2x^2 - 4x - 2)/2
    g(x + 1) = -x^2 - 2x - 1

    Misal
    x + 1 = a
    x = a - 1

    g(a) = -(a - 1)^2 - 2(a - 1) - 1
    g(a) = -(a^2 - a - a + 1) - 2a + 2 - 1
    g(a) = -a^2 + 2a - 1 - 2a + 1
    g(x) = -x^2

    y = -x^2
    -y = x^2
    x = √-y
    g invers (x) = √-x

    g invers (-2) = √-(-2)
    g invers (-2) = √2

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