Question

DIK: G(X) = X+3
(FOG)(X) = X^2+6X+7

DIT: (GOF)(X)=????????????

Answer 1

Verified answer

Fungsi Komposisi
--------------------------

Cara Mengerjakan :
g (x) = x + 3

(fog) (x) = x² + 6x + 7
f {g (x)} = x² + 6x + 7
f (x + 3) = x² + 6x + 7
Misal :
y = x + 3
x = y - 3

f (x + 3) = x² + 6x + 7
f (y) = (y - 3)² + 6 (y - 3) + 7
f (y) = (y² - 6y + 9) + 6y - 18 + 7
f (y) = y² - 2
f (x) = x² - 2

Maka ,
(gof) (x) = g {f (x)}
= g (x² - 2)
= (x² - 2) + 3
= x² + 1 ------> Ini jawabannya

Semoga bisa bermanfaat
HHNS

Answer 2

Bab Fungsi Komposisi
Matematika SMA Kelas X

(fog) (x) = x²  + 6x + 7
f(x + 3) = x² + 6x + 7
f(x - 3 + 3) = (x - 3)² + 6 (x - 3) + 7
f(x) = x² - 6x + 9 + 6x - 18 + 7
f(x) = x² - 2

(gof) (x) = g(x²- 2)
(gof) (x) = x² - 2 + 3
(gof) (x) = x² + 1