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