Diketahui f(x) =x-3 dan (g of) (x) =x2+6x+9 maka g(x-1)=

Bab Fungsi Komposisi dan Invers
Matematika SMA

(g o f)(x) = x²+6x+9
(g o f)(x) = (x+3)²
g(f(x)) = (x+3)²
g(x-3) = (x+3)²
g(x-3) = (x-3+6)²
g(x) = (x+6)²

sehingga

g(x-1) = (x-1+6)²
g(x-1) = (x+5)²
g(x-1) = x²+10x+25

Mapel : Matematika
Kelas : X SMA
Bab : Fungsi Komposisi dan Fungsi Invers

Pembahasan :
Gof(x) = x² + 6x + 9
G(f(x)) = x² + 6x + 9
G(x - 3) = x² + 6x + 9

Misal x - 3 = a
x = a + 3

G(a) = (a + 3)² + 6(a + 3) + 9
G(a) = a² + 6a + 9 + 6a + 18 + 9
G(a) = a² + 12a + 36
G(x - 1) = (x - 1)² + 12(x - 1) + 36
G(x - 1) = x² - 2x + 1 + 12x - 12 + 36
G(x - 1) = x² + 10x + 25