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If $R$ denotes the set of all real numbers then the function $f: R \rightarrow R$ defined $f(x)=[x]$
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Neither one-one nor onto
Let $f\left(x_1\right)=f\left(x_2\right) \Rightarrow\left[x_1\right]=\left[x_2\right] \Rightarrow x_1=x_2$
{For example, if $x_1=1.4, x_2=1.5$, then [1.4]=[1.5] =1}
$\therefore f$ is not one-one.
Also, $f$ is not onto as its range I (set of integers) is a proper subset of its co-domain $R$.
{For example, if $x_1=1.4, x_2=1.5$, then [1.4]=[1.5] =1}
$\therefore f$ is not one-one.
Also, $f$ is not onto as its range I (set of integers) is a proper subset of its co-domain $R$.
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