Diketahui fog(x) = 3xkuadrat - 22x + 38 dan f(x) = 3x kuadrat + 2x - 2 Tentukan g(x) ! Thanks

dik: (fog) (x) = 3x² - 22x + 38; f(x) = 3x² + 2x - 2;
dit: g(x)?
jawab:
(fog) (x) = f(g(x)) = 3x² - 22x + 38

f(x) = 3x² + 2x - 2
f(g(x)) = 3(g(x))² + 2(g(x)) - 2

3x² - 22x + 38 = 3(g(x))² + 2(g(x)) - 2
3(g(x))² + 2(g(x)) = 3x² - 22x + 40 |:3
(g(x))² + 2(g(x))/3 = x² - 22x/3 + 40/3 |+1/9
(g(x))² + 2(g(x))/3 + 1/9 = x² - 22x/3 + 40/3 + 1/9
(g(x) + 1/3)² = x² - 22x/3 + 121/9
g(x) + 1/3 = ± √(x² - 22x/3 + 121/9)
g(x) = -1/3 ± √{(9x² - 66x + 121)/9}
g(x) = {-1 ± √(9x² - 66x + 121)}/3
g(x) = {-1 ± √(3x - 11)²}/3
g(x) = {-1 + (3x - 11)}/3
g(x) = {3x - 12}/3
g(x) = x - 4