Question

Kelas 10
bab fungsi
kategori fungsi invers

soal di lampiran, yg no 11

Answer 1

Verified answer

Kelas 10 Matematika
Bab Fungsi Komposisi

(fog) (x) = 1/(x - 2) . √(x² - 4x + 5)
y = 1/(x - 2) . √(x² - 4x + 5)
(x - 2) . y = √(x² - 4x + 5)
(xy - 2y)² = √(x² - 4x + 5)²
(xy)² - 2xy . 2y + (2y)² = x² - 4x + 5
x²y² - 4xy² + 4y² - x² + 4x = 5
x²y² - x² - 4xy² + 4x = -4y² + 5
x² (y² - 1) - 4x (y² - 1) = -4y² + 5
(x² - 4x) (y² - 1) = -4y² + 5
x² - 4x = (-4y² + 5)/(y² - 1)
x² - 4x + 4 = ((-4y² + 5)/(y² - 1)) + 4
(x - 2)² = (-4y² + 5 + 4(y² - 1))/(y² - 1)
x - 2 = √((-4y² + 5 + 4y² - 4)/(y² - 1))
x = 2 +- √(1/(y² - 1))
(fog)^-1 (x) = 2 +- √(1/(x² - 1))

atau

x = 2 +- √(1/(y² - 1))
x = 2 +- 1/√(y² - 1)
x = 2 +- (1/(y² - 1)) . √(y² - 1)
(fog)^-1 (x) = 2 +- (1/(x² - 1)) . √(x² - 1)