Answer to Question #225298 in Discrete Mathematics for Ripon Chandra

Question

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

Answer 1

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.