diketahui f (x) =x , g (x) =x-3 dan h (x) = 5x tentukan : a. (f . (g . h ) ) (x) b. ((f . g ) .h ) (x)

Mapel : Matematika
Kelas : X SMA
Bab : Fungsi Komposisi dan Fungsi Invers

Pembahasan :
A. (F o (g o h))(x) = f(g(h(x))
(F o (g o h))(x) = f(5x - 3)
(F o (g o h))(x) = (5x - 3)²
(F o (g o h))(x) = 25x² - 30x + 9

B. ((F o g) o h)(x) = fog h(x)
((F o g) o h)(x) = fog(5x)
((F o g) o h)(x) = f(g(5x))
((F o g) o h)(x) = f(5x - 3)
((F o g) o h)(x) = (5x - 3)²
((F o g) o h)(x) = 25x² - 30x + 9

f(x) = x^2
g(x) = x - 3
h(x) = 5x

a.
(g○h)(x) = g(h(x))
...............= g(5x)
...............= 5x - 3
(f○(g○h))(x) = f((g○h)(x))
.....................= f(5x - 3)
.....................= (5x - 3)^2
.....................= 25x^2 - 30x + 9
(f○(g○h))(x) = 25x^2 - 30x + 9

b.
(f○g)(x) = f(g(x))
..............= f(x - 3)
..............= (x - 3)^2
..............= x^2 - 6x + 9
((f○g)○h)(x) = f○g(h(x))
.....................= f○g(5x)
.....................= (5x)^2 - 6(5x) + 9
.....................= 25x^2 - 30x + 9
((f○g)○h)(x) = 25x^2 - 30x + 9