Show that the function \( f: \mathbf{R} \rightarrow\{x \in \mathbf{...

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Show that the function \( f: \mathbf{R} \rightarrow\{x \in \mathbf{R}:-1x1\} \) defined by \( f(x)=\frac{x}{1+|x|}, x \in \mathbf{R} \) is one one and onto function.
\( \mathrm{P} \)
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