F(x)= 3x + 2 dan g(x)= x^2 - 2x + 6 tentukan rumus untuk : a. (f o g)(x) b. (g o f)(x)

Kelas 10 Matematika
Bab Fungsi Komposisi

a] (fog) (x) = f(x² - 2x + 6)
(fog) (x) = 3 (x² - 2x + 6) + 2
(fog) (x) = 3x² - 6x + 18 + 2
(fog) (x) = 3x² - 6x + 20

b] (gof) (x) = g(3x + 2)
(gof) (x) = (3x + 2)² - 2(3x + 2) + 6
(gof) (x) = 9x² + 12x + 4 - 6x - 4 + 6
(gof) (x) = 9x² + 6x + 6

a. (f o g) (x)=f(g(x)
=3x+2
=3(x^2-2x+6) +2
=3x^2-6x+18+2
=3x^2-6x+20

b. (g o f) (x) =g(f(x)
=x^2x+6
=(3x+2) ^2-2(3x+2) +6
=9x^2+12x+4-6x-4+6
=9x^2+6x+6