Question

Check the injectivity and surjectivity of the function:
$f:N\to N$ given by $f\left(x\right)=x^2$.

Answer 1

$f:N\to N$

$f\left(x\right)=x^2$

For $xϵN,$ $f\left(x\right)ϵN$

But $f\left(x\right)\subset N$

So $f(x) is into, thus not subjective.

$xϵN$

$f\left(x\right)$ attains different values for different values of $x$.

$thus$f(x)$ is one-one.

So, $f\left(x\right)$ is injective but not subjective.