Show that the function \(f: R \rightarrow x \in R:-1<x<1\) defined by \(f(x)=\frac{x}{1+|x...

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