Mohon bantuan nya 1. jika f(x-1) = x² - 1 dan g(x) = 3x maka nilai (g o f)(x) = ........... 2. ⁴log 2 + ⁴log 4 + ⁴log 16 = ................. 3. jika x₁ dan x₂ a

Mapel : Matematika
Kelas : X SMA
Bab : Fungsi , Logaritma dan Persamaan Kuadrat

Pembahasan :
1.
f(x - 1) = x² - 1

Misal x - 1 = a —» x = a + 1
f(a) = (a + 1)² - 1
f(a) = a² + 2a + 1 - 1
f(a) = a² + 2a

Gof(x) = g(f(x))
Gof(x) = 3(x² + 2x)
Gof(x) = 3x² + 6x

————————————————
2.

⁴log 2 + ⁴log 4 + ⁴log 16
= 1/2 + 1 + 2
= (1 + 2 + 4)/2
= 7/2

————————————————
3.

2x² + ax + (a - 1) = 0

Berdasarkan Teorema Vietta
x₁ + x₂ = -b/a
x₁ + x₂ = -a/2

x₁ . x₂ = c/a
x₁ . x₂ = (a - 1)/2

Maka....
x₁² + x₂² = 4
(x₁ + x₂)² - 2(x₁ . x₂) = 4
(-a/2)² - 2(a - 1)/2 = 4
(a²/4) - a + 1 = 4
a² - 4a + 4 = 16
a² - 4a - 12 = 0
(a - 6)(a + 2) = 0
a = 6
a = -2