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Matematika
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Pertanyaan
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1 Jawaban
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1. Jawaban Nissa1852
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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