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Trigonometry — Medium JEE math MCQ

If the function $f: \mathbb{R} \rightarrow \mathbb{R}$ is defined by $f(x)=|x|(x-\sin x)$, then which of the following statements is TRUE?
  1. A. $f$ is one-one, but NOT onto
  2. B. $f$ is onto, but NOT one-one
  3. C. $f$ is BOTH one-one and onto
  4. D. $f$ is NEITHER one-one NOR onto

Solution

The correct option is **C**.

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If the function f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} is defined by f(x)=∣x∣(x−sin⁡x)f(x)=|x|(x-\sin x), then which of the following statements is TRUE?
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Trigonometry — Medium JEE Mathematics MCQ | MyGoalPrep