Question

1. F(x) = -3x + 1 dan g(x) = 2x / x – 1 maka (g-1 ○ f-1)(x) = ...
A. X + 1 / x + 5
B. X + 1 / x – 5
C. X – 1 / x – 5
D. X – 1 / x + 5
E. X / x + 5

Answer 1

(g⁻¹of⁻¹)(x) = (fog)⁻¹(x)

(fog)(x) = f(g(x))
= -3(2x/(x-1)) + 1
= (-6x/(x-1)) + (x-1)/(x-1)
= (-5x-1)/(x-1)

y = (-5x - 1)/(x-1)
xy - y = -5x - 1
xy + 5x = y - 1
(y + 5)x = y - 1
x = (y - 1)/(y + 5)
(fog)⁻¹(x) = (x - 1)/(x + 5)
(g⁻¹of⁻¹)(x) = (x - 1)/(x + 5)