Answer to Question #224739 in Discrete Mathematics for ripon

Question

Determine whether the function f(x) = x^2 + 3x + 2 from Z to Z is a bijective

function.

Answer 1

The function $f(x)=x^2+3x+2$ is not one-to-one.

For example

$0\in Z, -3\in Z$

$$f(0)=(0)^2+3(0)+2=2$$

$$f(-3)=(-3)^2+3(-3)+2=2$$

Hence

$$f(0)=2=f(3)$$

Since the function $f(x)=x^2+3x+2$ is not one-to-one, then the given function is not bijective.