Question

Jika g(x) = x+3 dan (fog)(x) = x² - 4 ,maka f(x-2)

Answer 1

Diketahui :
F(x) = x² - 4
Maka f(x-2)
= (x-2)² - 4
= x² - 4x + 4 - 4
= x² - 4x

Maaf kalo salah

Answer 2

G(x) = x+3
(fog)(x) = x²-4
f(x) = ax²+bx+c

(fog)(x) = f(g(x))
x²-4 = a(x+3)²+b(x+3)+c
x²-4 = ax²+6ax+9a+bx+3b+c
x²-4 = ax²+(6a+b)x+(9a+3b+c)

samakan koefisien n konstanta:
x²→ 1 = a

x → 0 = 6a+b
       0 = 6+b
       b = -6

c → -4 = 9a+3b+c
       -4 = 9-16+c
        c = -3

f(x) = x² - 6x - 3
f(x-2) = (x-2)² - 6(x-2) - 3
         = (x²-4x+4) - 6x+12 - 3
         = x² - 10x + 13