Jika f(x) = 5x + 6, dan (g o f)(x) = x^2 - 3x, maka g(x) adalah ? Jawabannya ada gk ?

Kelas 10 Matematika
Bab Fungsi Komposisi

(gof) (x) = x² - 3x
g(5x + 6) = x² - 3x
g(5 . x/5 + 6) = (x/5)² - 3 . x/5
g(x + 6) = x²/25 - 3x/5
g(x - 6 + 6) = (x - 6)²/25 - 3 . (x - 6)/5
g(x) = (x² - 12x + 36)/25 - (15x - 90)/25
g(x) = (x² - 12x - 15x + 36 + 90)/25
g(x) = (x² - 27x + 126)/25

gof(x) = x^2 - 3x
g(f(x)) = x^2 - 3x
g(5x+6) = x^2 - 3x
misal 5x+6= a
maka x = (a - 6)/5
g(a) = [ (a - 6)/5 ]^2 - 3 ((a - 6)/5)
= ( a^2 - 12a + 36 )/25 - 15 (a-6)/25
= ( a^2 - 12a + 36 - 15a + 90) / 25
= ( a^2 - 27a + 126) / 25
g(x) = ( x^2 - 27x + 126) / 25