Matematika

Pertanyaan

tolong di jawab semoga semoga dibalas oleh allah
tolong di jawab semoga semoga dibalas oleh allah

1 Jawaban

  • No.2

    f(x) = 3x + 1  ;  x < 0
             x² + 1   ;  0 ≤ x < 2
             2x + 3  ;  x ≥ 2
    maka
    f(-1) + f(1) + f(3)
    = [3(-1) + 1] + [1² + 1] + [2(3) + 3]
    = -2 + 2 + 9
    = 9

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    No. 3

    f(x) = 2x² - 2x + 14
    g(x) = x² + x

    fog(x)
    = f(g(x))
    = f(x² + x)
    = 2(x² + x)² - 2(x² + x) + 14
    = 2(x⁴ + 2x³ + x²) - 2x² - 2x + 14
    = 2x⁴ + 4x³ + 2x² - 2x² - 2x + 14
    = 2x⁴ + 4x³ - 2x + 14

    fog(-1)
    = 2(-1)⁴ + 4(-1)³ - 2(-1) + 14
    = 2 - 4 + 2 + 14
    = 14

    -----------------------------------------------------------------------------------------

    No. 4
    A.
    f(x) = 24x + 12
    y = 24x + 12
    y - 12 = 24x
    (y - 12)/24 = x
    jadi
    f⁻¹(x) = (x - 12) / 24

    B.
    f(x) = (9x - 5) / 12x
    y = (9x - 5) / 12x
    12xy = (9x - 5)
    12xy - 9x = -5
    x (12y - 9) = -5
    x = -5 / (12y - 9)
    jadi 
    f⁻¹(x) = -5 / (12x - 9)

    -----------------------------------------------------------------------------

    No.5
    A.
    f(x)= 2x + 7
    y = 2x + 7
    y - 7 = 2x
    (y - 7) / 2 = x
    jadi
    f
    ⁻¹(x) = (x - 7) / 2

    B.
    g(x)= 3 / 2x
    y = 3 / 2x
    2xy = 3
    x = 3/2y
    jadi 
    g⁻¹(x) = 3 / 2x