diketahui f-1=3x+4, g(x)=4x-5/2x-5,nilai g-1of-1(x) adalah... caranya ya

f-¹(x) = 3x + 4
g(x)= 4x-5 / 2x-5
g-¹(x)
↓
y = 4x -5 / 2x-5
y(2x-5)=4x-5
2xy-5y=4x-5
3xy-4x=5y-5
x(3y-4)=5y-5
x= 5y-5 / 3y-4
g-¹(x) = 5x-4 / 3x-4

maka
(g-¹of-¹)(x)
5(f-¹(x) ) - 4 / 3(f-¹(x)) -4
5(3x - 4)-4 / 3(3x-4)-4
15x-20-4 / 9x-12-4
15x-24 / 9x-16

jadi
(g-¹of-¹)(x) = 15x-24 / 9x-16

mencari g^-1 (x) terlebih dahulu

g(x) = (4x -5) / (2x -5)
y = (4x -5) / (2x -5)
y(2x -5) = 4x -5
2xy -5y = 4x -5
3xy -4x = 5y -5
x(3y -4) = 5y -5
x= (5y -5) / (3y -4)
g^-1 (x) = 5x -4 / 3x -4

mencari (g^-1 o f^-1)(x)

= g^-1 (f^-1 (x))
= g^-1 (3x +4)
= (5(3x +4) -4) / (3(3x +4) -4)
= (15x +20 -4) / (9x +12 -4)
= (15x +16) / (9x +8)