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Show that the function \( f: \mathbf{R}_{*} \rightarrow \mathbf{R}_{*} \) defined by \( f(x)=\frac{1}{x} \) is one-one and onto, where \( \mathbf{R}_{*} \) is the set of all non-zero real numbers. Is the result true, if the domain
\( \mathrm{P} \) \( \mathbf{R}_{*} \) is replaced by \( \mathbf{N} \) with co-domain being same as \( \mathbf{R}_{*} \) ?

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