# Mark (√) against the correct answer in the following:

Question:

Mark (√) against the correct answer in the following:

$f: N \rightarrow N: f(x)=2 x$ is

A. one - one and onto

B. one - one and into

C. many - one and onto

D. many - one and into

Solution:

$f(x)=2 x$

For One - One

$f\left(x_{1}\right)=2 x_{1}$

$f\left(x_{2}\right)=2 x_{2}$

put $f\left(x_{1}\right)=f\left(x_{2}\right)$ we get

$2 x_{1}=2 x_{2}$

Hence, if $f\left(x_{1}\right)=f\left(x_{2}\right), x_{1}=x_{2}$

Function $\mathrm{f}$ is one - one

For Onto

$f(x)=2 x$

let $f(x)=y$, such that $y \in N$

$2 x=y$

$\Rightarrow \mathrm{X}=\frac{\mathrm{y}}{2}$

If $y=1$

$x=\frac{1}{2}=0.5$

which is not possible as $x \in N$

Hence, $f$ is not onto., $f$ is into

Hence, option b is correct