jika (fog) (x)=4x²+8x-3 dan g(x)=2x+4,maka tentukan f-¹(x)

(f • g)(x) = 4x^2 + 8x - 3
g(x) = 2x + 4

Misalkan: a = 2x + 4 = g(x)
2x = a - 4


(f • g)(x) = f(g(x))
4x^2 + 8x - 3 = f(a)
(2x)^2 + 4(2x) - 3 = f(a)
(a - 4)^2 + 4(a - 4) - 3 = f(a)
a^2 - 8a + 16 + 4a - 16 - 3 = f(a)
a^2 - 4a - 3 = f(a)
f(x) = x^2 - 4x - 3

f(x) = y
x^2 - 4x - 3 = y
x^2 - 4x = y + 3
x^2 - 4x + 4 = y + 3 + 4
(x - 2)^2 = y + 7
x - 2 = akar(y + 7)
x = -2 + akar(y + 7)
f(x)^-1 = -2 + akar(x + 7)