JEE Advanced 2025 Paper 1 Mathematics Q3

Mathematics

Problem

Let ℝ denote the set of all real numbers. Define the function f : ℝ → ℝ by f(x) = 2 − 2x² − x² sin(1/x) if x ≠ 0, and f(x) = 2 if x = 0. Then which one of the following statements is TRUE?

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