jika diketahui g(x)= 2x+3/3x dan (gof-1)(x) = 4x-1/2x+3 maka f(x) adalah

Fungsi invers komposisi

g(x) = (2x+3)/(3x)
{gof⁻¹)(x) = (4x-1)/(2x+3)
misal f⁻¹(x)= y

g {f⁻¹(x)} = (4x -1)/(2x+3)
{2. y +3} /{3.y}  = (4x - 1) / (2x + 3)
(2. y + 3)(2x + 3) = { 3.y (4 x -1)}
4xy + 6y + 6x + 9 = 12xy - 3y
4xy -12xy +6y + 3y =- 9
-8 xy  +9y = - 9
y  (-8x + 9) = -9
y = -9/(-8x + 9)
f⁻¹(x)= -9/(-8x +9)

f(x)= (9x + 9)/(8x)