Indicate whether the two functions are equal.

If the two functions are not equal, then give an element of the domain on which the two functions have different values.

$f:Z\to Z,$ where $f\left(x\right)=\left|x+y\right|$

$g:Z\to Z,$ where $g\left(x\right)=\left|x\right|+\left|y\right|$

Indicate whether the two functions are equal. If the two functions are not equal, then give an element of the domain on which the two functions have different values.

$f:Z\to Z,$ where $f\left(x\right)=x^3$

$g:Z\to Z,$ where $g\left(x\right)={\left|x\right|}^3$

Give an example of two functions $f:N\to Z$ and $g:Z\to Z$ such that gof is injective but g is not injective.