Which of the following functions from Z into Z are bijectives?

The correct answer is Option (2) → $f(x)=x+2$ ##

Here, $f(x)=x+2$

Let $f(x_1)=f(x_2)$

$⇒x_1+2=x_2+2$

$⇒x_1=x_2$

Let $y=x+2$

then, $x=y-2∈Z\,∀\,y∈Z$