Question

Jika f(x) : 3x – 2
(g ○ f ) (x) = - 24x + 5

Tentukan
A. g(x) = ?
B. (F○g) (x) = ?

Answer 1

(g ○ f ) (x) = 18x^2 - 24x + 5
g(f(x)) = 18x^2 - 24x + 5
g(3x-2)= 18x^2 - 24x + 5
g(x) = 18((x+2)/3)²-24(x+2)/3+5
g(x) = 2(x+2)² - 8(x+2) + 5
g(x) = 2(x²+4x+4)-8x-16+5
g(x) = 2x²+8x+8-8x-11
g(x) = 2x²-3

Answer 2

Cari (x)
y = 3x - 2
y + 2 = 3x
x= (y + 2)/3
(x) = (x + 2)/3

g(x) = (g o f)((x))
= 18((x + 2)/3)² - 24 ((x + 2)/3) + 5
= 18(x² + 4x + 4)/9 - 24 (x + 2)/3 + 5
= 2x² + 8x + 8 - 8x - 16 + 5
= 2x² - 3

(f o g)(x) = 3 (2x² - 3) - 2
= 6x² - 9 - 2 = 6x² - 11