Diketahui f(x)= 4x + 2 dan ( fog ) (x) =4x2 + 6. Tentukan fungsi g(x)=?

f(x) = 4x + 2
(fog)(x) = 4x² + 6

maka
(fog)(x) = 4x² + 6
f(g(x)) = 4x² + 6
4g(x) + 2 = 4x² + 6
4g(x) = 4x² + 4
g(x) = 4x²/4 + 4/4
g(x) = x² + 1

diberikan:

[tex]f(x)=4x+2\quad\text{dan}\quad (f\circ g)(x)=4x^2+6[/tex]

[tex](f\circ g)(x)=4x^2+6 \\ \\ f(g(x))=4x^2+6 \\ \\ 4g(x)+2=4x^2+6 \\ \\ 4g(x)=4x^2+6-2 \\ 4g(x)=4x^2+4 \\ \\ g(x)=\frac{4x^2+4}{4} \\ \\ g(x)=x^2+1[/tex]