Matematika

Pertanyaan

Fungsi g dinyatakan dgn
g(x)=x^+px+q.Jika nilai g(3)=-8 dan g(-2)=7
Tentukan :
A.nilai p dan q
B.bentuk fungsi g
C.nilai g(-6)+g(4)

1 Jawaban

  • g(x) = x² + px + q
    g(3) = 3² + 3p + q
    - 8 = 9 + 3p + q
    3p + q = - 8 - 9
    3p + q = - 17
    g(-2) = (-2)² + p(-2) + q
    7 = 4 - 2p + q
    - 2p + q = 7 - 4
    - 2p + q = 3

    3p + q = - 17
    - 2p + q = 3
    -------------------(-)
    5p = - 20
    p = - 4

    3p + q = - 17
    3(-4) + q = - 17
    - 12 + q = - 17
    q = - 17 + 12
    q = - 5

    b) g(x) = x² - 4x - 5

    c) g(-6) = (-6)² - 4(-6) - 5 = 36 + 24 - 5 = 55
    g(-2) = (-2)² - 4(-2) - 5 = 4 + 8 - 5 = 7
    g(-6) + g(-2) = 55 + 7 = 62

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