Question

Diketahui f(x) = 3x-1 dan (gof)(x) = 9x² - 6x + 4 maka (fog)(x) =......?
tolong di bantu ya beserta caranya

Answer 1

(gof)(x) = 9x²-6x+4
g(f(x)) = 9x²-6x+4
g(3x-1) = 9x²-6x+4
misal 3x-1 = a
x = (a+1) : 3
jadi
g(a) = 9 ((a+1) : 3)² -6 ((a+1) : 3) +4
= 9 ( (a² +2a+1) :9) - 6 ((a+1) : 3) +4
= ( a² +2a+1) - 2(a+1) +4
= a² +2a+1 -2a -2 +4
= a² + 3
g(x) = x² + 3

nah,
(fog)(x) = f(g(x))
= 3( x² +3) -1
= 3x² + 9 -1
= 3x² + 8