Given $ f: R \rightarrow R$ defined by $f(x)=[x],$ where $[x]$ denotes the greatest integer $leq x$:
For example, if we consider $x=1.1$, we see that $f(1.1) = 1$.
Similarly, if we consider $x = 1.9$, we see that $f(1.9) = 1$.
$\Rightarrow [1.1]=[1.9]$, but given $1.1 \neq 1.9$, $f$ is not one-one.
Let us consider $x = 0.7 \in R \rightarrow [x] = 0$.
Since it is given that $[x]$ denotes the greates integer $\leq x$, there can be no element such that $f(x) = 0.7$.
Therefore, $f$ is not onto.
Solution: $f$ is neither one-one nor onto.