Jika f(x) = x^2 + 1 dan g(x) = x+1, maka (fog) (x) - (gof) (x) A. 2g(x) B.2g(x)-3 C. 2g(x+1)-4
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Pertanyaan
Jika f(x) = x^2 + 1 dan g(x) = x+1, maka (fog) (x) - (gof) (x)
A. 2g(x)
B.2g(x)-3
C. 2g(x+1)-4
A. 2g(x)
B.2g(x)-3
C. 2g(x+1)-4
1 Jawaban
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1. Jawaban Yuki0
F(g(x)) = f(x+1)
= (x+1)^2 + 1
= x^2 + 2x + 1 + 1
= x^2 + 2x + 2
G(f(x)) = g(x^2+1)
= x^2 + 1 + 1
= x^2 + 2
(Fog)(x) - (gof)(x)
= x^2 + 2x + 2 - (x^2 + 2)
= x^2 + 2x + 2 - x^2 - 2
= 2x
Jawaban dalam bentuk g(x)
G(x) = x+1
X = G(x) - 1
2x = 2(g(x) - 1)
= 2g(x) - 2