jika f(x)=2x/5x-1 dan g^-1(x)= 3/7x+4 tentukan rumus untuk (fog)^-1(x)

langsung aja y

fof`¹(x) = x
f{f`¹(x)} = x
2f`¹(x) / 5f`¹(x) - 1 = x
2f`¹(x) = 5x.f`¹(x) - x
5x.f`¹(x) - 2f`¹(x) = x
f`¹(x) (5x - 2) = x
f`¹(x) = x / 5x-2

g`¹(x) = 3 / 7x+4

maka
(fog)`¹(x) = g`¹of`¹(x)

= g`¹{f`¹(x)}
= 3 / 7f`¹(x) + 4
= 3 / 7(x/5x-2) + 4
= 3 / 7x / 5x-2 + 4
= 3 : 7x/5x-2 + 4
= 3 : (7x+4(5x-2) / 5x-2
= 3 : (7x+20x-8) / 5x-2
= 3 × 5x-2 / 27x - 8
= (15x - 6) / (27x - 8)

semoga berguna +_+