Show that the function defined by is one-one and onto

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

1. 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

\mathbf{R}_{*}

is replaced by

\mathbf{N}

with co-domain being same as

\mathbf{R}_{*}