Matematika

Pertanyaan

tolong bantu jawab ya
tolong bantu jawab ya

1 Jawaban

  • f(x) = (x^2 - 2x + 5)/(x^2 + x)
    asimtot tegak f(x)
    x^2 + x = 0
    x(x + 1) = 0
    x = 0 atau x = -1

    g(x) = (3x^2 - 4)/(x^2 + bx + c)
    asimtot tegak g(x)
    x^2 + bx + c = 0, b < 0

    asimtot tegak g(x) berjarak 1 satuan dan 2 satuan dg salah satu asimtot tegak fungsi f
    Ada beberapa kemungkinan:
    1) berjarak 1 satuan dengan x = 0 => x = 1 dan x = -1
    berjarak 2 satuan dengan x = 0 => x = 2 dan x = -2
    (a) x = 1 dan x = 2 => (x - 1)(x - 2) = x^2 - 3x + 2 => memenuhi karena b < 0
    (b) x = 1 dan x = -2 => (x - 1)(x + 2) = x^2 + x - 2 => tdk memenuhi krn b > 0
    (c) x = -1 dan x = 2 => (x + 1)(x - 2) = x^2 - x - 2 => memenuhi krn b < 0
    (d) x = -1 dan x = -2 => (x + 1)(x + 2) = x^2 + 3x + 2 => tdk memenuhi krn b > 0

    2) berjarak 1 satuan dg x = -1 => x = 0 dan x = -2
    berjarak 2 satuan dg x = -1 => x = 1 dan x = -3
    (a) x = 0 dan x = 1 => x(x - 1) = x^2 - x => memenuhi krn b < 0
    (b) x = 0 dan x = -3 => x(x + 3) = x^2 + 3x => tdk memenuhi krn b > 0
    (c) x = -2 dan x = 1 => (x + 2)(x - 1) = x^2 + x - 2 => tdk memenuhi krn b > 0
    (d) x = -2 dan x = -3 => (x + 2)(x + 3) = x^2 + 5x + 6 => tdk memenuhi krn b > 0

    jadi yg memenuhi
    1a) x^2 - 3x + 2 = 0 => b + c = -3 + 2 = -1
    1c) x^2 - x - 2 = 0 => b + c = -1 - 2 = -3
    2a) x^2 - x = 0 => b + c = -1 + 0 = -1