f(x) = 2x + 6 , g(x) = x + 6 , h(x) = x + 2 . tentukan gog(x) , foh(x) , gof(x) , fogoh(x) , gofoh(x) , hogof(x) , hofog(x) . tolong jawab dong?

Mapel : Matematika
Kelas 11 SMA
Fungsi Komposisi

Rumus :
Jika 2 fungsi f(x) dan g(x) maka :
(f•g)(x) = f(g(x))

Penyelesaian :
Dik :
f(x) = 2x + 6
g(x) = x+6
h(x) = x+2

Nomor. 1
(g•g) (x) = (x+6) + 6
(g•g) (x) = x + 12

Nomor 2.
(f•h) (x) = 2(x+2) + 6
(f•h) (x) = 2x + 4 + 6
(f•h) (x) = 2x + 10

Nomor 3.
(g•f) (x) = (2x+6) + 6
(g•f) (x) = 2x + 12

Nomor 4.
(f•g•h) (x) = [f(g•h)(x)]
(f•g•h) (x) = f [(x+2)+6]
(f•g•h) (x) = f(x+8)
(f•g•h) (x) = 2 (x+8)
(f•g•h) (x) = 2x + 16

Nomor 5.
(g•f•h) (x) = [g(f•h)(x)]
(g•f•h) (x) = g (2x+10)
(g•f•h) (x) = (2x+10) + 6
(g•f•h) (x) = 2x + 16

Nomor 6
(h•g•f) (x) = [h(g•f)(x)]
(h•g•f) (x) = h (2x+12)
(h•g•f) (x) = (2x+12) + 2
(h•g•f) (x) = 2x + 14

Nomor 7.
(h•f•g) (x) = [h(f•g)(x)]
(h•f•g) (x) = h [2(x+6)+6]
(h•f•g) (x) = h (2x+12+6)
(h•f•g) (x) = h (2x+18)
(h•f•g) (x) = (2x+18) + 2
(h•f•g) (x) = 2x + 20

Semoga membantu.