jika f(x) = 2x + 4 / 3x - 2 dan g(x) = 2x - 1 maka tentukan rumus (f bundaran g)^-1 (x)
Matematika
katreen1
Pertanyaan
jika f(x) = 2x + 4 / 3x - 2 dan g(x) = 2x - 1 maka tentukan rumus (f bundaran g)^-1 (x)
1 Jawaban
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1. Jawaban whongaliem
f (x) = (2x + 4) / (3x - 2) dan g (x) = 2x - 1
(f o g) (x) = f (g (x))
= f (2x - 1)
= {2 (2x - 1) + 4} / {3(2x - 1) - 2}
= (4x - 2 + 4) / (6x - 3 - 2)
= (4x - 2) / (6x - 5)
y = (4x - 2) / (6x - 5)
y (6x - 5) = 4x - 2
6xy - 5y = 4x - 2
6xy - 4x = 5y - 2
x (6y - 4) = 5y - 2
x = (5y - 2) / (6y - 4)
(fog)^-1 (x) = (5x - 2) / (6x - 4)