If $\mathrm{R}$ denotes the set of all real numbers then the function $\mathrm{f}: \mathrm{R} \rightarrow…
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
injective and surjective.
neither injective nor surjective.
injective.
surjective.
Solution
$\begin{aligned} & \mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}, \mathrm{f}(\mathrm{x})=|\mathrm{x}| \\ & \because \mathrm{f}(-1)=\mathrm{f}(1)=1\end{aligned}$
i.e. not injection
and range of $\mathrm{f}(\mathrm{x})$ is $[0, \infty]$
Hence, not surjection