COMEDK 2025 Afternoon Solved Paper

Concept:Completing the square transforms the quadratic to find its minimum value on the given domain.Explanation:Rewrite $f(x)$ by completing the square:$f(x) = x^2 - 4x + 5 = (x-2)^2 + 1$.The domain is $x \ge 2$.For $x \ge 2$, the term $(x-2)^2 \ge 0$.Thus the smallest possible value of $f(x)$ occurs when $(x-2)^2 = 0$, i.e., at $x = 2$, giving $f(2) = 1$.As $x$ increases beyond 2, $(x-2)^2$ grows without bound, so $f(x) \to \infty$.Hence $f(x)$ takes all values from $1$ upwards.Therefore the range is $[1, \infty)$.Answer:Option D: $[1,\infty)$