Question

Prove that the Greatest integer function $f:R\to R$ given by $f\left(x\right)=\left[x\right]$, is neither one-one nor onto, where $\left[x\right]$ denotes the greatest integer less than or equal to $x$.

Answer 1

For $f:R\to R$

where $f\left(x\right)=\left[x\right]$

Graph of $f\left(x\right)$ is shown above.

So, by using graph we can say that $f\left(x\right)$ is nither one-one nor onto.