Matematika

Pertanyaan

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1 Jawaban

  • f (x) = 2x+6
    g(x) = x+3
    h(x) = x+2
    1).( f°g ) = f(g(x))
    = f (x+3)
    = 2(x+3) + 6
    = 2x + 6 + 6
    = 2x + 12
    2). g°f = g(f(x))
    =  g(2x+6)
    = 2x + 6 + 3
    = 2x + 9
    3). f°f = f(f(x))
    = f (2x+6)
    = 2 (2x+6) + 6
    = 4x + 12 + 6
    = 4x + 18
    4). g°g= g(g(x))
    = g(x+3)
    = x+3 + 3
    = x +6
    5). f°h = f(h(x))
    = f (x+2)
    = 2 (x+2) + 6
    = 2x + 4 + 6
    = 2x + 10
    6). g°f = g(f(x))
    =  g(2x+6)
    = 2x + 6 + 3
    = 2x + 9
    7). f°g°h = f(g(h(x)))
    = f(g(x+2))
    = f(x+2+3)
    = f(x+5)
    = 2 (x+5) + 6
    = 2x + 10 + 6
    = 2x + 16
    8). g°f°h = g(f(h(x)))
    = g(f(x+2))
    = g(2(x+2) + 6)
    = g(2x + 4 + 6)
    = g(2x + 10)
    = 2x+10 + 3
    = 2x + 13
    9). h°g°f = h (g(f(x)))
    = h (g(2x+6))
    = h(2x+6+3)
    = h(2x+9)
    = 2x+9+2
    = 2x + 11
    10). h°f°g = h (f(g(x)))
    = h(f(x+3))
    = h(2(x+3) + 6)
    = h (2x+6+6)
    = h (2x+12)
    = 2x+12+2
    = 2x + 14
    f°g(x) = 4x + 13
    g(x) = x+6
    g⁻¹(x) = x-6
    f°g(x) = 4x + 13
    f(g(x)) = 4x+13
    f(x+3) = 4x + 13
    f(x) = 4 (x-6) + 13
    f(x) = 4x - 24 + 13
    f(x) = 4x - 11
    2).misal g⁻¹(x) = y
    g(x)= x+6
    g⁻¹(x) = x + 6
    y = x + 6
    y - 6 = x  (g⁻¹(y))
    g⁻¹(x) = x - 6
    3). misal f⁻¹(x) = y
    f(x) = 4x -11
    f⁻¹(x) = 4x-11
    y = 4x - 11
    y + 11 = 4x
    y + 11/4 = x (f⁻¹(y))
    f⁻¹(x) = x + 11/4
    4). f⁻¹°g (x) = f⁻¹(g(x))
    = f⁻¹ (x+6)
    = x + 6 + 11/4
    = x + 17/4
    5). f⁰g⁻¹(x) = f(g⁻¹(x))
    = f (x-6)
    = 4(x-6) - 11
    = 4x - 24 - 11
    = 4x - 35
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