diketahui g o f(x) = -4x² - 12x - 8 dan f(x) = 2x + 3 tentukan g(x)==

Kelas 10 Matematika
Bab Fungsi Komposisi

(gof) (x) = -4x² - 12x - 8
g(2x + 3) = -4x² - 12x - 8
g(2 . x/2 + 3) = -4 (x/2)² - 12 . (x/2) - 8
g(x + 3) = -4 x²/4 - 6x - 8
g(x - 3 + 3) = - (x - 3)² - 6 (x - 3) - 8
g(x) = - (x² - 6x + 9) - 6x + 18 - 8
g(x) = -x² + 6x - 9 - 6x + 10
g(x) = -x² + 1

Fungsi Komposisi

gof(x) = -4x^2 - 12x - 8
g(f(x)) = -4x^2 - 12x - 8
g(2x+3) = -4x^2 - 12x - 8

dimisalkan 2x+3 = a
maka, x = (a-3)/2

g(a) = -4((a-3)/2)^2 - 12(a-3)/2 - 8
= -4 ((a^2-6a+9)/4) - 6(a-3) - 8
= - a^2 + 6a - 9 - 6a + 18 - 8
= - a^2 + 1
maka,

g(x) = - x^2 +1

Semoga bisa dipahami.