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Question: Answered & Verified by Expert
If $\mathrm{R}$ denotes the set of all real numbers then the function $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ defined by $f(x)=|x|$ is
MathematicsFunctionsMHT CETMHT CET 2022 (05 Aug Shift 2)
Options:
  • A injective and surjective.
  • B neither injective nor surjective.
  • C injective.
  • D surjective.
Solution:
2825 Upvotes Verified Answer
The correct answer is: neither injective nor surjective.
$\begin{aligned} & \mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}, \mathrm{f}(\mathrm{x})=|\mathrm{x}| \\ & \because \mathrm{f}(-1)=\mathrm{f}(1)=1\end{aligned}$
i.e. not injection
and range of $\mathrm{f}(\mathrm{x})$ is $[0, \infty]$
Hence, not surjection

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