# Q.3 Prove that the Greatest Integer Function $f : R\longrightarrow R$, given by $f (x) = [x]$, is neither one-one nor onto, where $[x]$ denotes the greatest integer less than or equal to $x$.

$f : R\longrightarrow R$

$f (x) = [x]$

One- one:

For   $1.5,1.7 \in R$   then $f(1.5)=\left [ 1.5 \right ] = 1$     and    $f(1.7)=\left [ 1.7 \right ] = 1$

but   $1.5\neq 1.7$

$\therefore$  f is not one- one i.e. not injective.

For  $0.6 \in R$  there is no x in R such that $f(x)=\left [ 0.6 \right ]$

$\therefore$  f is not onto i.e. not surjective.

Hence, f is not injective but not surjective.

## Related Chapters

### Preparation Products

##### JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
##### Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
##### Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
##### Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-