f(x)=x^2-nx dan g(x)=3x+14 nilai yang memenuhi (fog)(-4)=(gof)(2)

Pertama tama, tentukan dulu (f o g)(x) dan (gof)(x).
(fog)(x) = f(g(x)) = (3x + 14)² - n(3x + 14)
= 9x² + 84x + 196 - 3nx - 14n
= 9x² + (84 - 3n)x + (196 - 14n)
(gof)(x) = g(f(x)) = 3(x² - nx) + 14 = 3x² - 3nx + 14
(fog)(-4) = 9(-4)² + (84 - 3n)(-4) + (196 - 14n) = 144 - 336 + 12n + 196 - 14n
= 4 - 2n
(gof)(2) = 3(2)² - 3n(2) + 14 = 12 - 6n + 14 = 26 - 6n
(fog)(-4) = (gof)(2)
4 - 2n = 26 - 6n
-2n + 6n = 26 - 4
4n = 22
n = 22/4 = 11/2 = 5½