diketahui f(x) = x-2, g(x) = x kuadrat + 3x- 7, dan h(x) = 5x + 6. tentukan p jika (g komposisi f) (p) = (h komposisi g) (p)!
Jawaban Terkonfirmasi
F(x) = x – 2. —–> f(p) = p – 2
g(x) = x² + 3x – 7 ——> g(p) = p² + 3p – 7
h(x) = 5x + 6 —–> h(p) = 5p + 6
(g o f) (p) = (h o g) (p)
g(p – 2) = h(p² + 3p – 7)
(p – 2)² + 3(p – 2) – 7 = 5(p² + 3p – 7) + 6
p² – 4p + 4 + 3p – 6 – 7 = 5p² + 15p – 35 + 6
p² – p – 9 = 5p² + 15p – 29
5p² – p² + 15p + p – 29 + 9 = 0
4p² + 16p – 20 = 0
Semua bagi 4 maka
p² + 4p – 5 = 0
(p + 5) (p – 1) = 0
p = -5 V p = 1