diketahui FX kurangi 2 = x kuadrat + 3 x dan GX = 4 x + 1 ditanya rumus fungsi f Bundaran GX

Kelas 10 Matematika
Bab Fungsi Komposisi

f(x - 2) = x² + 3x
f(x + 2 - 2) = (x + 2)² + 3 (x + 2)
f(x) = x² + 4x + 4 + 3x + 6
f(x) = x² + 7x + 10

(fog) (x) = f(g(x))
(fog) (x) = f(4x + 1)
(fog) (x) = (4x + 1)² + 7(4x + 1) + 10
(fog) (x) = 16x² + 8x + 1 + 28x + 7 + 10
(fog) (x) = 16x² + 36x + 18

Diketahui :
f(x-2) = x^2 + 3x
g (x) = 4x + 1

Ditanya : fog (x) = .... ?

Penyelesaian :

Terlebih dahulu cari f(x)

f (x-2) = x^2 + 3x
misal x-2 = a, maka x = a+2
f(a) = (a+2)^2 + 3 (a+2)
f(a) = a^2 + 4a + 4 + 3a + 6
f(a) = a^2 + 7a + 10
f(x) = x^2 + 7x + 10

kemudian cari fog (x)

fog(x) = f(g(x))=f(4x+1)=(4x+1)^2 + 7 (4x+1) + 10
= 16x^2 + 8x + 1 + 28x + 7 + 10
= 16x^2 + 36x + 18

semoga dapat dipahami.
Jangan lupa minum air putih 8 gelas sehari.