If $f: \mathbb{R} \to \mathbb{R}$ is defined by $f(x) = x^2 - 3x + 2$, write $f(f(x))$.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $x^4 - 6x^3 + 10x^2 - 3x$ ##
Given that,
$f(x) = x^2 - 3x + 2$
$∴f(f(x)) = f(x^2 - 3x + 2)$
$= (x^2 - 3x + 2)^2 - 3(x^2 - 3x + 2) + 2$
$= x^4 + 9x^2 + 4 - 6x^3 - 12x + 4x^2 - 3x^2 + 9x - 6 + 2$
$= x^4 + 10x^2 - 6x^3 - 3x$
$∴f(f(x)) = x^4 - 6x^3 + 10x^2 - 3x$