Matematika

Pertanyaan

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1 Jawaban

  • 1.
    f(x) = a + 2x
    g(x) = bx - 6
    f(0) = g(3) = 9

    #mncari nilai a dan b
    f(0) = 9
    a + 2(0) = 9
    a = 9

    g(3) = 9
    bx - 6 = 9
    3b = 9+6
    b = 15/3
    b= 5

    =>>subsitusi nilai a dan b ke pers. f(x) dan g(x)

    f(x) = 2x + 9 ,,, g(x) = 5x - 6

    #(g○f)(x) = 5 (2x + 9) - 6
    = 10x + 45 - 6
    = 10x + 39
    (g○f)(-3) = 10 (-3) + 39
    = -30 + 39 = 9

    #g(x) invers
    [tex] {g}^{ - 1} (x) = 5x - 6 \\ y = 5x - 6 \\ 5x = y + 6 \\ x = \frac{y + 6}{5} \\ {g}^{ - 1} (x) = \frac{x + 6}{5} \\ \\ jadi \\ {g}^{ - 1} (4) = \frac{4 + 6}{5} = \frac{10}{5} = 2[/tex]