Question

Function $f:R\to R,f\left(x\right)=\left[x\right]$ is

• A. one-one
• B. onto
• C. one-one onto
• D. Many one into

Answer 1

The correct option is D Many one into

For $x=0.1,f\left(x\right)=\left[0.1\right]=0$

For $x=0.2,f\left(x\right)=\left[0.2\right]=0$

$\Rightarrow f\left(x\right)$ is not one-one.

For each $f\left(x\right)\in R,$ there exists $x\in R$ such that $\left[x\right]=y.$
Therefore $f\left(x\right)$ is onto.

Hence : $R\to R$ is onto but not one-one.