f(x)=2x-4 dan (g o f) = 4xkuadrat-24x+32 tentukan g(x)

f invers (x) = x+4 / 2
karena f o f invers = identitas,
maka g o f o f invers = g (x)
jadi g (x) = 4 (x+4/2)^2 -24(x+4/2) +32
g (x) = 4 ( x^2+8x+ 4 /4 ) - 12 (x+4) +32
= x^2 + 8x + 4 - 12x - 48 + 32
= x^2 - 4x - 12

f(x) = 2x - 4
(g o f)(x) = 4x^2 - 24x + 32
g(f(x)) = 4x^2 - 24x + 32
g(2x - 4) = 4x^2 - 24x + 32
Misal (2x - 4) = a => 2x = a + 4 => x = (a + 4)/2
g(a) = 4((a + 4)/2)^2 - 24(a + 4)/2 + 32
g(a) = 4(a^2 + 8a + 16)/4 - 12(a + 4) + 32
g(a) = a^2 + 8a + 16 - 12a - 48 + 32
g(a) = a^2 - 4a
g(x) = x^2 - 4x

^ = pangkat