Jika diketahui fungsi g(x) = 2x + 6 dan (f o g)(x) = 4x² + 22x + 18, rumus fungsi f(x) adalah ...

Bab Fungsi

(f o g)(x) = 4x² + 22x + 18
f(g(x)) = 4x² + 22x + 18
f(2x + 6) = 4x² + 22x + 18

Misalkan
2x + 6 = a
Maka
2x = a - 6
x = (a - 6)/2

Substitusikan ke dalam fungsi
f(a) = [tex] 4(\frac{a-6}{2} )^{2} + 22 (\frac{a - 6}{2} ) + 18[/tex]
f(a) = [tex] 4(\frac{ a^{2} -12x + 36}{4} )} + 11(a - 6) + 18[/tex]
f(a) = [tex] a^{2} -12x + 36 + 11a - 66 + 18[/tex]
f(x) = [tex] x^{2} -x -12[/tex]

(fog) (x) = 4x²+22x+18
f(2x+6)=4x²+22x+18
misal
t = 2x+6
2x = t-6
x = t-6 / 2
sehingga
f(x) = 4(t-6 / 2)²+22(t-6 / 2)+18
=(t²-12t+36)+11t-66+18
=t²-t-12
f(x) = x²-x-12