Question

Diketahui : f(x) = x + 2 dan g(x) = x² - 2x + 3.
Tentukan :
A. (f ° g)(x)
B. (f ° f)(x)
C. (g ° f)(x)

Answer 1

Jawab:

Penjelasan dengan langkah-langkah:

Diketahui :

f(x) = x + 2 dan g(x) = x² - 2x + 3

Ditanya :

a) (f o g)(x)

b) (f o f)(x)

c) (g o f)(x)

Pembahasan :

a) (f o g)(x)

(f o g)(x) = f( g(x) )

(f o g)(x) = f(x² - 2x + 3)

(f o g)(x) = x² - 2x + 3 + 2

(f o g)(x) = x² - 2x + 5

Sehingga (f o g)(x) = x² - 2x + 5.

b) (f o f)(x)

(f o f)(x) = f( f(x) )

(f o f)(x) = f(x + 2)

(f o f)(x) = x + 2 + 2

(f o f)(x) = x + 4

Sehingga (f o f)(x) = x + 4.

c) (g o f)(x)

(g o f)(x) = g( f(x) )

(g o f)(x) = g(x + 2)

(g o f)(x) = (x+2)² - 2(x+2) + 2

(g o f)(x) = x² + 4x + 4 - 2x - 4 + 2

(g o f)(x) = x² + 2x + 2

Sehingga (g o f)(x) = x² + 2x + 2.