g(x)=3x-2 (fog) (x)= 3x²-3x+2 f(1)= ....
Matematika
niaputri16
Pertanyaan
g(x)=3x-2
(fog) (x)= 3x²-3x+2
f(1)= ....
(fog) (x)= 3x²-3x+2
f(1)= ....
1 Jawaban
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1. Jawaban aliakbar20
g(x) = 3x - 2
(fog)(x) = 3x² - 3x + 2
Misal:
3x - 2 = a ⇔ untuk ruas kiri
x = (a + 2)/3 ⇔ untuk ruas kanan
(fog)(x) = 3x² - 3x + 2
f(g(x)) = 3x² - 3x + 2
f(3x - 2) = 3x² - 3x + 2
Subtitusi:
f(3x - 2) = 3x² - 3x + 2
f(a) = 3((a + 2)/3)² - 3((a + 2)/3) + 2
f(a) = 3((a² + 4a + 4)/9) - (a + 2) + 2
f(a) = (a² + 4a + 4)/3 - a + 2 + 2
f(a) = (a² + 4a + 4)/3 - a + 4
f(x) = (x² + 4x + 4)/3 - x + 4