Diketahui f(x) = x²-x-6 dan g(x) =x²+2 Tentukan fog dan gof

fog(x) = f(g(x)) = f(x² + 2) = (x² + 2)² - (x² + 2) - 6
= x^4 + 4x² + 4 - x² - 2 - 6
= x^4 + 3x² - 4
gof(x) = g(f(x)) = g(x² - x - 6) = (x² - x - 6)² + 2
= x^4 - 2x³ - 11x² + 12x + 38

f(x) = x²-x-6
g(x) = x²+2

(fog)(x) = f[g(x)]
= (x²+2)²-(x²+2)-6
= x⁴+4x²+4-x²-2-6
= x⁴+4x²-x²+4-2-6
= x⁴+3x-4

(gof)(x) = g[f(x)]
= (x²-x-6)²+2
= x⁴-2x³-11x²+12x+36+2
= x⁴-2x³-11x²+12x+38