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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
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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
i.e. not injection
and range of $\mathrm{f}(\mathrm{x})$ is $[0, \infty]$
Hence, not surjection
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