( f o g ) (x) = 2x - 1 g (x) = 3x + 1 f (x) = ???

Kelas 10 Matematika
Bab Fungsi Komposisi

(fog) (x) = 2x - 1
f (3x +1) = 2x - 1
f (3 . x/3 + 1) = 2 . x/3 - 1
f (x + 1) = (2x/3) - 1
f (x - 1 + 1) = (2 . (x - 1)/3) - 1
f (x) = (2x - 2)/3 - 1
f (x) = (2x/3) - 2/3 - 1
f (x) = (2x/3) - 1 2/3

Diketahui:
(f o g)(x) = 2x - 1
g(x) = 3x + 1

Ditanya:
f(x) = ?

Pembahasan:
Buat permisalan dulu
3x + 1 = a (untuk ruas kiri)
x = (a - 1)/3 (untuk ruas kanan)

Dari definisi (fog)(x)
(f o g)(x) = 2x - 1
f(g(x)) = 2x - 1
f(3x + 1) = 2x - 1

Masukkan permisalan tadi
f(3x + 1) = 2x - 1
f(a) = 2{(a - 1)/3} - 1
f(a) = (2a - 2)/3 - 1
f(a) = 2a/3 - 2/3 - 3/3
f(a) = ⅔a - 5/3
f(a) = ⅔a - 1⅔

Jadi
f(x) = ⅔x - 1⅔