UPSC NDA II 2025 Mathematics Paper

Concept:The cube root function is defined for all real numbers, so the expression inside the cube root can be any real value.Explanation:For $f(x)=1-\sqrt[3]{(x-1)^{2}}$, note that $(x-1)^{2}$ is always non‑negative for any real $x$.The cube root of a real number is always a real number, regardless of the sign of the radicand.Thus, there is no restriction on $x$. Every real number gives a valid output.Hence, the domain is the entire set of real numbers.Answer:Option B: $(-\infty, \infty)$ is correct.