Question

1. Diketahui dua fungsi f dan g yang masing-masing dirumuskan sebagai f(x) = x²-4x +3 dan g(x) = 6-2x. Tentukan rumus fungsi-funsi berikut beserta domainnya :
a. (f x g) (x)
b. (f/g) (x)

2. Dik : h(x) = dan g(x) = 4-2x.
Dit : Rumus fungsi dan domain dari :
a. (h + g) (x)
b. (h - g) (x)
c. (h x g) (x)
d. (h/g) (x)

Mohon Bantuannya :)

Answer 1

Verified answer

Kelas 10 Matematika
Bab Fungsi komposisis

Nomor 1
a] (f . g) (x) 
= (x² - 4x + 3) . (6 - 2x)
= 6x² - 2x³ - 24x + 8x² + 18 - 6x
= -2x³ + 14x² - 30x + 18

b] (f / g) (x) 
= (x² - 4x + 3) / (6 - 2x)
= ((x - 1) (x - 3)) / (-2 . (x - 3))
= (x - 1)/-2
= (1 - x)/2

Nomor 2
h(x) = (2x - 5)/(x + 3) dan g(x) = 4 - 2x

a] (h + g) (x)
= (2x - 5)/(x + 3) + 4 - 2x
= (2x - 5 + (4 - 2x) . (x + 3))/(x + 3)
= (2x - 5 + 4x + 12 - 2x² - 6x)/(x + 3)
= (-2x² + 7)/(x + 3)

b] (h - g) (x)
= (2x - 5)/(x + 3) - (4 - 2x)
= (2x - 5 - (4 - 2x) . (x + 3))/(x + 3)
= (2x - 5 - (4x + 12 - 2x² - 6x))/(x + 3)
= (2x - 5 - (-2x² - 2x + 12))/(x + 3)
= (2x - 5 + 2x² + 2x - 12)/(x + 3)
= (2x² - 17)/(x + 3)

c] (h . g) (x) 
= (2x - 5)/(x + 3) . (4 - 2x)
= (8x - 4x² - 20 + 10x)/(x + 3)
= (-4x² + 18x - 20)/(x + 3)

d] ( h / g) (x)
= ((2x - 5)/(x + 3)) / (4 - 2x)
= (2x - 5)/(4x - 2x² + 12 - 6x)
= (2x - 5)/(-2x² - 2x + 12)