Question

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

note : (^) pangkat

Answer 1

(fog) (x) = f(g(x))
x^4 - 4x^2 + 4 = f(x^2-2)

dimisalkan
x^2-2 = p
x^2 = p + 2
x = akar p + 2
⇩
f(p) = (akar p+2)^4 - 4(akar p+2)^2 + 4
= p^2 + 4p + 4 - 4p - 8 + 4
= p^2

jadi f(x) = x^2

maaf kalo salah