diketahui f(x) =3x-1 per x+2, x tidak = -2 dan g(x) =2x+5 per x-3, x tidak =3. tentukan (fog)^-1(x)

f(x) = (3x - 1)/(x + 2), g(x) = (2x + 5)/(x - 3)
(f o g)(x) = f(g(x))
= (3g(x) - 1)/(g(x) + 2)
= (3(2x + 5)/(x - 3) - 1) / ((2x + 5)/(x - 3) + 2) . (x - 3)/(x - 3)
= (3(2x + 5) - 1(x - 3)) / (2x + 5 + 2(x - 3))
= (6x + 15 - x + 3) / (2x + 5 + 2x - 6)
= (5x + 18)/(4x - 1)

(f o g)^-1(x) = (x + 18)/(4x - 5) ; x ≠ 5/4