UPSC NDA II 2023 Mathematics Solved Paper

Concept:The domain of a function is the set of all real inputs for which the function gives a real output.For $f(x)=\sqrt{2-x}+\sqrt{2+x}$, both square roots require the expressions inside to be non-negative.Explanation:For $\sqrt{2-x}$ to be defined, $2-x \ge 0$ must hold.This gives $x \le 2$.For $\sqrt{2+x}$ to be defined, $2+x \ge 0$ must hold.This gives $x \ge -2$.The function is defined only when both conditions are true simultaneously.Therefore, $x$ must satisfy $x \le 2$ and $x \ge -2$, i.e., $-2 \le x \le 2$.This includes all numbers from $-2$ to $2$, including the endpoints.Answer:$[-2, 2]$