Matematika Fungsi Invers No 11 dan 12

11) f(x) = 1 + 4x - x²
y = 1 + 4x - x²
x² - 4x = 1 - y
(x² - 4x + 4) = 1 - y + 4
(x - 2)² = 5 - y
x - 2 = ± √5 - y
x = 2 ± √(5 - y)
f-¹(x) = 2 ± √5 - x


2) f(x) = 5ˣ

g(x) = x² + 3

dit : f⁻¹ [g(25) - 3]

1) cari fungsi g(25) - 3
g(25) - 3 = (25² + 3) - 3 = 625 + 3 - 3 = 625
f [g(25) - 3] = f(625)

2) cari invers dari f(x) = 5ˣ
f(x) = 5ˣ
y = 5ˣ
x = ⁵log y
f⁻¹(x) = ⁵log x

3) substitusi
f⁻¹ (625) = ⁵log 625
f⁻¹ (625) = ⁵log 5⁴
f⁻¹ (625) = 4

maka
f⁻¹ [g(25) - 3] = 4