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

The function $f\left(x\right)=x+2$ is one-one as for ${\mathbf{x}}_1,{\mathbf{x}}_2\in Z$

Consider, $f\left(x_1\right)=f\left(x_2\right)$

$\begin{array}{l}\Rightarrow x_1+2=x_2+2\\ \Rightarrow x_1=x_2\end{array}$

Also, let $y\in$ codomain of $f=Z$ such that $y=f\left(x\right)$

$\begin{array}{l}\Rightarrow y=x+2\\ \Rightarrow x=y-2\in Z\text{ for all }y\in Z\end{array}$

$\therefore f$ is onto.

Hence, $f\left(x\right)=x+2$ is bijective.