Determine whether the function f(x) = |4x| from Z to Z is a bijective function.

The function $f(x)=|4x|$ is not one-to-one.

For example

$-1\in Z, 1\in Z$

$f(-1)=|4(-1)|=4$

$f(1)=|4(1)|=4$

Hence

$f(-1)=4=f(1)$

Since the function $f(x)=|4x|$ is not one-to-one, then the given function is not bijective.