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Let $f$ be a function from the set of natural numbers to the set of even natural numbers given by $f(x)=2 x$. Then $f$ is
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both one-one and onto
$1 ..... 2$
$2 ..... 4$
$3 ..... 6$
$4 ..... 8$
Domain (x) $\quad$ Co-domain $(2 \mathrm{x})$ For each element in the domain there is only one element in the therefore $\mathrm{f}(\mathrm{x})$ is one-one. No image in the co-domain which has no pre-image in the domain, therefore $\mathrm{f}(\mathrm{x})$ is onto Hence $\mathrm{f}(\mathrm{x})$ both is one-one and onto.
$2 ..... 4$
$3 ..... 6$
$4 ..... 8$
Domain (x) $\quad$ Co-domain $(2 \mathrm{x})$ For each element in the domain there is only one element in the therefore $\mathrm{f}(\mathrm{x})$ is one-one. No image in the co-domain which has no pre-image in the domain, therefore $\mathrm{f}(\mathrm{x})$ is onto Hence $\mathrm{f}(\mathrm{x})$ both is one-one and onto.
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