f(x)= 2x + 1 dan (fog)(x+1)= -2xkuadrat - 4x - 1 nilai g invers (-2) ?
Matematika
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Pertanyaan
f(x)= 2x + 1 dan (fog)(x+1)= -2xkuadrat - 4x - 1 nilai g invers (-2) ?
1 Jawaban
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1. Jawaban dewa251202
(f ○ g)(x + 1) = f(g(x + 1))
-2x^2 - 4x - 1 = 2(g(x + 1)) + 1
2(g(x + 1)) = -2x^2 - 4x - 1 - 1
g(x + 1) = (-2x^2 - 4x - 2)/2
g(x + 1) = -x^2 - 2x - 1
Misal
x + 1 = a
x = a - 1
g(a) = -(a - 1)^2 - 2(a - 1) - 1
g(a) = -(a^2 - a - a + 1) - 2a + 2 - 1
g(a) = -a^2 + 2a - 1 - 2a + 1
g(x) = -x^2
y = -x^2
-y = x^2
x = √-y
g invers (x) = √-x
g invers (-2) = √-(-2)
g invers (-2) = √2