Jika f(x)=2x-1,g(x)=x^2-3x+1,dan (f o g) (p) =9,nilai p adalah
Matematika
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Pertanyaan
Jika f(x)=2x-1,g(x)=x^2-3x+1,dan (f o g) (p) =9,nilai p adalah
2 Jawaban
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1. Jawaban dewa251202
Cari rumus (f ○ g)(x) -nya dulu
(f ○ g)(x)
= f(g(x))
= 2(x^2 - 3x + 1) -1
= 2x^2 - 6x + 2 - 1
= 2x^2 - 6x + 1
(f ○ g)(p) = 2p^2 - 6p + 1
9 = 2p^2 - 6p + 1
0 = 2p^2 - 6p + 1 - 9
2p^2 - 6p - 8 = 0
2p^2 - 8p + 2p - 8 = 0
2p(p - 4)+2(p - 4) = 0
(2p + 2)(p - 4) = 0
HP = {(-1,4)}
Jadi, p = -1 atau p = 4 -
2. Jawaban rinajuniw
f(x) = 2x-1
g(x) = x²-3x+1
(fog)(p) = f[g(p)]
9 = 2(p²-3p+1)-1
9 = 2p²-6p+2-1
9 = 2p²-6p+1
0 = 2p²-6p+1-9
0 = 2p²-6p-8
= (2p-8)(p+1)
p = 4 atau p = -1
maaf ya kalo salah