Question

Check the injectivity and surjectivity of the following functions:$f:Z\to Z$ given by $f\left(x\right)=x^2$

Answer 1

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

It is seen that $f(-1)=f\left(1\right)=1$, but $-1\ne 1$
$\therefore f$ is not injective.

Now, $-2\in Z$. But, there does not exist any

element $x\in Z$ such that $f\left(x\right)=x^2=-2$

$\therefore f$ is not surjective.

Hence, function $f$ is neither injective nor surjective.