Functions $f, g : R \to R$ are defined, respectively, by $f(x) = x^2 + 3x + 1$, $g(x) = 2x - 3$, find $fog$.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $4x^2 - 6x + 1$ ##
Given that, $f(x) = x^2 + 3x + 1, g(x) = 2x - 3$
$fog(x) = f\{g(x)\} = f(2x - 3)$
$= (2x - 3)^2 + 3(2x - 3) + 1$
$= 4x^2 + 9 - 12x + 6x - 9 + 1 = 4x^2 - 6x + 1$