jika diketahui fungsi g(x) = 2x+6 dan (fog)(x)=4x^2+22x+18, rumus fungsi f adalah

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

Ditanya :
f(x)

Jawaban :

misalkan :
y = 2x + 6
[tex] \frac{y - 6}{2} = x[/tex]
Maka,
[tex]f(g(x)) = {4x}^{2} + 22x + 18 \\ f( g(x) ) = 4 (\frac{x - 6}{2} )^{2} + 22( g(x) ) + 18 \\ f(g(x) ) = 4( \frac{ {x}^{2} - 12x + 36 }{4} ) + 11x - 66 + 18 \\ f( g(x) ) = {x}^{2} - 12x + 36 + 11x - 66 + 18 \\ f( g(x) ) = {x}^{2} - x - 12 [/tex]
Jadi, f(x) = x² - x - 12