Question

Diketahui f (x)= akar x^2 + 1 dan (fog) (x)= 1/x-2 akar x^2-4x+5. Tentukanlah (fog)^-1 (x).

Answer 1

Verified answer

(fog)-¹(x) invers dari fog(x)
1/x-2 (√x²-4x+5) = y
√x²-4x+5 = y(x-2)
kuadratkan kedua ruas
x² - 4x + 5 = y²(x - 2)²
(x - 2)² + 1 = y²(x - 2)²
1 = y²(x - 2)² - (x - 2)²
1 = (y² - 1)(x - 2)²
1/(y² - 1) = (x - 2)²
(x - 2)² = 1/(y² - 1)
x - 2 = √{1/(y² - 1)}
x = 2 + √{1/(y² - 1)}
(fog)-¹(x) = 2 + √{1/(x² - 1)}